diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index e9e2ac7..6ad0d46 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -14,6 +14,8 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
+        package: [ "gap-actions/ActionTestGAPDocPackage", "gap-actions/ActionTestOldDocPackage" ]
+        affix: [ 1, 2 ] # Run each package twice, to check reproducibility
         include:
           - package: "gap-actions/ActionTestGAPDocPackage"
             force: true
@@ -53,6 +55,56 @@ jobs:
         with:
           dry-run: true
           force: ${{ matrix.force }}
+          _affix: "-${{ matrix.affix }}"
+
+  check-reproducibility:
+    name: "Check if builds are reproducible"
+    runs-on: ubuntu-latest
+    needs: test-action
+    strategy:
+      fail-fast: false
+      matrix:
+        package: [ "ActionTestGAPDocPackage", "ActionTestOldDocPackage" ]
+    steps:
+    
+      - name: "Download releases"
+        uses: actions/download-artifact@v8
+        with:
+          pattern: "Release_assets_for_${{ matrix.package }}*"
+          path: ${{ runner.temp }}
+          
+      - name: "Compare releases"
+        shell: bash
+        working-directory: ${{ runner.temp }}
+        run: |
+          # Move downloaded assets
+          # The .zip is not an extension but part of the directory name
+          mv Release_assets_for_*-1.zip v1
+          mv Release_assets_for_*-2.zip v2
+
+          error_found=false
+          for EXT in .tar.gz .tar.bz2 .zip; do
+            for file1 in v1/*"$EXT"; do
+              file2="v2/$(basename "$file1")"
+
+              # Calculate sha256 checksums
+              chk1=$(sha256sum "$file1" | cut -d' ' -f1)
+              chk2=$(sha256sum "$file2" | cut -d' ' -f1)
+            
+              if [[ "$chk1" != "$chk2" ]]; then
+                echo "::error::Checksum mismatch for ${EXT} archives"
+                echo "v1: $chk1"
+                echo "v2: $chk2"
+                error_found=true
+              else
+                echo "${EXT} archives are reproducible"
+              fi
+            done
+          done
+
+          if ${error_found}; then
+            exit 1
+          fi
 
   test-scripts:
     name: "Test the scripts used by this action"
diff --git a/action.yml b/action.yml
index 733ff41..55b186a 100644
--- a/action.yml
+++ b/action.yml
@@ -14,6 +14,10 @@ inputs:
     description: "Body text for the new GitHub release that will appear on the package's GitHub Releases page"
     required: false
     default: "Release of ${{ github.event.repository.name }}"
+  _affix:
+    description: "UNDOCUMENTED, FOR INTERNAL USE ONLY. Required for testing to ensure unique artifact names"
+    required: false
+    default: ""
 
 runs:
   using: "composite"
@@ -162,7 +166,7 @@ runs:
     - name: "Run autogen.sh"
       shell: bash
       working-directory: ${{ runner.temp }}/${{ env.BASENAME }}
-      run : |
+      run: |
         if [ -x autogen.sh ] ; then
           sudo apt-get install autoconf automake build-essential --yes
           echo "Generating build system files"
@@ -173,7 +177,7 @@ runs:
     - name: "Check for symlinks"
       shell: bash
       working-directory: ${{ runner.temp }}/${{ env.BASENAME }}
-      run : |
+      run: |
         $GITHUB_ACTION_PATH/scripts/check_symlinks.sh || {
           echo "::error::Symlinks detected"
           exit 1
@@ -192,13 +196,27 @@ runs:
       shell: bash
       working-directory: ${{ runner.temp }}
       run: |
+        # Get release date
+        DATEFORMAT=$(echo "${DATE}" | awk -F/ '{print $3"-"$2"-"$1}')
+        SOURCE_DATE_EPOCH=$(date -d "$DATEFORMAT" +%s)
+        
+        # Note that we change file modification times / sorting / ... to obtain reproducible builds
+        # Recommendations taken from https://reproducible-builds.org/docs/archives/
+        find $BASENAME -print0 | xargs -0r touch --no-dereference --date="@${SOURCE_DATE_EPOCH}"
+        # Tar options
+        TAROPTS=(
+          --sort=name
+          --owner=0 --group=0 --numeric-owner
+          --pax-option=exthdr.name=%d/PaxHeaders/%f,delete=atime,delete=ctime
+          -cf - "${BASENAME}"
+        )
         for EXT in $ARCHIVE_FORMATS ; do
           ARCHIVENAME=$BASENAME$EXT
           echo "Creating $ARCHIVENAME ..."
           case $EXT in
-            .tar.gz)  tar cf - "$BASENAME" | gzip -9c > "$ASSETS/$ARCHIVENAME" ;;
-            .tar.bz2) tar cf - "$BASENAME" | bzip2 -9c > "$ASSETS/$ARCHIVENAME" ;;
-            .zip)     zip -r9 --quiet "$ASSETS/$ARCHIVENAME" "$BASENAME" ;;
+            .tar.gz)  tar "${TAROPTS[@]}" | gzip -9c > "$ASSETS/$ARCHIVENAME" ;;
+            .tar.bz2) tar "${TAROPTS[@]}" | bzip2 -9c > "$ASSETS/$ARCHIVENAME" ;;
+            .zip) find "$BASENAME" -print0 | LC_ALL=C sort -z | tr '\0' '\n' | zip -X -r9 --quiet "$ASSETS/$ARCHIVENAME" -@ ;;
             *)
               echo "::error::Unsupported archive format $EXT"
               exit 1
@@ -232,13 +250,13 @@ runs:
     - name: "Copy body-text"
       if: ${{ inputs.dry-run == 'true' }}
       shell: bash
-      run: echo "${{ inputs.body-text }}" > $RUNNER_TEMP/Release_text_for_${PKGNAME}_${VERSION}.md
+      run: echo "${{ inputs.body-text }}" > $RUNNER_TEMP/Release_text_for_${PKGNAME}_${VERSION}${{ inputs._affix }}.md
 
     - name: "Upload the release assets"
       uses: actions/upload-artifact@v7
       if: ${{ inputs.dry-run == 'true' }}
       with:
-        name: "Release_assets_for_${{ env.PKGNAME }}_${{ env.VERSION }}.zip"
+        name: "Release_assets_for_${{ env.PKGNAME }}_${{ env.VERSION }}${{ inputs._affix }}.zip"
         archive: true
         path: ${{ env.ASSETS }}/*
         if-no-files-found: error