diff --git a/src/debhelper/links/completion.rs b/src/debhelper/links/completion.rs
new file mode 100644
index 0000000..cde4c72
--- /dev/null
+++ b/src/debhelper/links/completion.rs
@@ -0,0 +1,122 @@
+use std::collections::BTreeMap;
+use std::path::Path;
+
+use tower_lsp_server::ls_types::{CompletionItem, CompletionItemKind, Position};
+
+use crate::debhelper::completion;
+
+/// Completions for a debian/links file at the given cursor position.
+pub fn get_completions(
+    text: &str,
+    position: Position,
+    package_dir: Option<&Path>,
+) -> Vec<CompletionItem> {
+    completion::get_completions(text, position, |_, prefix| match package_dir {
+        Some(dir) => package_candidates(dir, prefix),
+        None => Vec::new(),
+    })
+}
+
+/// Paths inside the package staging directory for a link token.
+fn package_candidates(package_dir: &Path, prefix: &str) -> Vec<CompletionItem> {
+    let dir = match prefix.rfind('/') {
+        Some(i) => &prefix[..=i],
+        None => "",
+    };
+    let mut found: BTreeMap<String, bool> = BTreeMap::new();
+    if let Ok(entries) = std::fs::read_dir(package_dir.join(dir)) {
+        for entry in entries.flatten() {
+            let name = entry.file_name();
+            let candidate = format!("{dir}{}", name.to_string_lossy());
+            if candidate.starts_with(prefix) {
+                let is_dir = entry.file_type().map(|t| t.is_dir()).unwrap_or(false);
+                found.insert(candidate, is_dir);
+            }
+        }
+    }
+    found
+        .into_iter()
+        .map(|(path, is_dir)| {
+            let (label, kind) = if is_dir {
+                (format!("{path}/"), CompletionItemKind::FOLDER)
+            } else {
+                (path, CompletionItemKind::FILE)
+            };
+            CompletionItem {
+                label,
+                kind: Some(kind),
+                ..Default::default()
+            }
+        })
+        .collect()
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn staging(files: &[&str]) -> tempfile::TempDir {
+        let dir = tempfile::tempdir().unwrap();
+        for rel in files {
+            let path = dir.path().join(rel);
+            std::fs::create_dir_all(path.parent().unwrap()).unwrap();
+            std::fs::write(&path, "").unwrap();
+        }
+        dir
+    }
+
+    fn labels(items: &[CompletionItem]) -> Vec<String> {
+        items.iter().map(|i| i.label.clone()).collect()
+    }
+
+    #[test]
+    fn completes_the_target_token() {
+        let pkg = staging(&["usr/bin/prog"]);
+        let items = get_completions("usr/\n", Position::new(0, 4), Some(pkg.path()));
+        assert!(labels(&items).contains(&"usr/bin/".to_string()));
+    }
+
+    #[test]
+    fn completes_the_link_token() {
+        let pkg = staging(&["usr/bin/prog"]);
+        let items = get_completions(
+            "usr/share/foo usr/\n",
+            Position::new(0, 18),
+            Some(pkg.path()),
+        );
+        assert!(labels(&items).iter().any(|l| l.starts_with("usr/")));
+    }
+
+    #[test]
+    fn a_later_token_still_completes() {
+        let pkg = staging(&["usr/bin/prog"]);
+        let items = get_completions("a b usr/\n", Position::new(0, 8), Some(pkg.path()));
+        assert!(labels(&items).iter().any(|l| l.starts_with("usr/")));
+    }
+
+    #[test]
+    fn directories_end_with_a_slash() {
+        let pkg = staging(&["usr/bin/prog"]);
+        let items = get_completions("usr", Position::new(0, 3), Some(pkg.path()));
+        let usr = items.iter().find(|i| i.label == "usr/").unwrap();
+        assert_eq!(usr.kind, Some(CompletionItemKind::FOLDER));
+    }
+
+    #[test]
+    fn nothing_without_a_package_dir() {
+        let items = get_completions("usr/\n", Position::new(0, 4), None);
+        assert!(items.is_empty());
+    }
+
+    #[test]
+    fn dollar_offers_substitution_vars() {
+        let items = get_completions("usr/lib/$\n", Position::new(0, 9), None);
+        assert!(items.iter().any(|i| i.label == "${DEB_HOST_MULTIARCH}"));
+    }
+
+    #[test]
+    fn no_completion_in_comment() {
+        let items = get_completions("# usr/share/foo\n", Position::new(0, 15), None);
+        assert!(items.is_empty());
+    }
+}
diff --git a/src/debhelper/links/detection.rs b/src/debhelper/links/detection.rs
new file mode 100644
index 0000000..3111950
--- /dev/null
+++ b/src/debhelper/links/detection.rs
@@ -0,0 +1,61 @@
+use std::path::{Path, PathBuf};
+
+use tower_lsp_server::ls_types::Uri;
+
+use crate::debhelper::detection::is_debhelper_file;
+
+/// Whether the URI is a debian/links or debian/<package>.links file.
+pub fn is_links_file(uri: &Uri) -> bool {
+    is_debhelper_file(uri, "links")
+}
+
+/// The staging directory whose files a links file refers to: debian/<package>
+/// for a debian/<package>.links file, else debian/tmp for a plain debian/links.
+pub fn package_dir(debian_dir: &Path, uri: &Uri) -> PathBuf {
+    match package_name(uri) {
+        Some(pkg) => debian_dir.join(pkg),
+        None => debian_dir.join("tmp"),
+    }
+}
+
+/// The <package> part of a debian/<package>.links filename, if any.
+fn package_name(uri: &Uri) -> Option<String> {
+    let file = uri.as_str().rsplit('/').next()?;
+    let stem = file.strip_suffix(".links")?;
+    (!stem.is_empty()).then(|| stem.to_string())
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn uri(s: &str) -> Uri {
+        s.parse().unwrap()
+    }
+
+    #[test]
+    fn detects_qualified_and_unqualified() {
+        assert!(is_links_file(&uri("file:///p/debian/links")));
+        assert!(is_links_file(&uri("file:///p/debian/mypkg.links")));
+    }
+
+    #[test]
+    fn package_dir_uses_the_package_name() {
+        let debian = Path::new("/p/debian");
+        assert_eq!(
+            package_dir(debian, &uri("file:///p/debian/mypkg.links")),
+            debian.join("mypkg")
+        );
+        assert_eq!(
+            package_dir(debian, &uri("file:///p/debian/links")),
+            debian.join("tmp")
+        );
+    }
+
+    #[test]
+    fn rejects_other_files() {
+        assert!(!is_links_file(&uri("file:///p/debian/control")));
+        assert!(!is_links_file(&uri("file:///p/links")));
+        assert!(!is_links_file(&uri("file:///p/debian/links.bak")));
+    }
+}
diff --git a/src/debhelper/links/mod.rs b/src/debhelper/links/mod.rs
new file mode 100644
index 0000000..b283cf4
--- /dev/null
+++ b/src/debhelper/links/mod.rs
@@ -0,0 +1,7 @@
+//! Support for debian/links and debian/<package>.links files.
+
+pub mod completion;
+pub mod detection;
+
+pub use completion::get_completions;
+pub use detection::{is_links_file, package_dir};
diff --git a/src/debhelper/mod.rs b/src/debhelper/mod.rs
index e20cc51..33c0e6a 100644
--- a/src/debhelper/mod.rs
+++ b/src/debhelper/mod.rs
@@ -7,6 +7,7 @@ pub mod docs;
 pub mod examples;
 pub mod info;
 pub mod install;
+pub mod links;
 pub mod manpages;
 pub mod not_installed;
 pub mod parser;
diff --git a/src/main.rs b/src/main.rs
index 24b8838..0ebe028 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -152,6 +152,8 @@ enum FileType {
     Install,
     /// debian/not-installed or debian/<package>.not-installed file
     NotInstalled,
+    /// debian/links or debian/<package>.links file
+    Links,
 }
 
 impl FileType {
@@ -203,6 +205,8 @@ impl FileType {
             Some(Self::Install)
         } else if debhelper::not_installed::is_not_installed_file(uri) {
             Some(Self::NotInstalled)
+        } else if debhelper::links::is_links_file(uri) {
+            Some(Self::Links)
         } else {
             None
         }
@@ -505,7 +509,8 @@ impl Backend {
             | FileType::Info
             | FileType::Manpages
             | FileType::Install
-            | FileType::NotInstalled => None,
+            | FileType::NotInstalled
+            | FileType::Links => None,
         }
     }
 
@@ -572,7 +577,8 @@ impl Backend {
             | FileType::Info
             | FileType::Manpages
             | FileType::Install
-            | FileType::NotInstalled => Vec::new(),
+            | FileType::NotInstalled
+            | FileType::Links => Vec::new(),
         }
     }
 
@@ -1553,6 +1559,13 @@ impl LanguageServer for Backend {
                     debian_dir.as_deref(),
                 )
             }
+            Some((FileType::Links, source_file)) => {
+                let workspace = self.workspace_clone().await;
+                let source_text = workspace.source_text(source_file);
+                let package_dir =
+                    Self::find_debian_dir(&uri).map(|d| debhelper::links::package_dir(&d, &uri));
+                debhelper::links::get_completions(&source_text, position, package_dir.as_deref())
+            }
             None => Vec::new(),
         };
 
@@ -2169,7 +2182,8 @@ impl LanguageServer for Backend {
             | FileType::Info
             | FileType::Manpages
             | FileType::Install
-            | FileType::NotInstalled => debhelper::semantic::generate_semantic_tokens(src),
+            | FileType::NotInstalled
+            | FileType::Links => debhelper::semantic::generate_semantic_tokens(src),
             FileType::Triggers => triggers::generate_semantic_tokens(src),
         };