procedure CompressFiles(Files : TStrings; const Filename : String);
var
 infile, outfile, tmpFile : TFileStream;
 compr : TZCompressionStream;
 i,l : Integer;
 s : String;
begin
  If Files.Count > 0 Then Begin
    outFile := TFileStream.Create(Filename,fmCreate);

    Try
      { the number of files }
      l := Files.Count;
      outfile.Write(l,SizeOf(l));

      For i := 0 to Files.Count-1 Do Begin
        infile := TFileStream.Create(Files[i],fmOpenRead);
        Try
          { the original filename }
          s := ExtractFilename(Files[i]);
          l := Length(s);
          outfile.Write(l,SizeOf(l));
          outfile.Write(s[1],l);

          { the original filesize }
          l := infile.Size;
          outfile.Write(l,SizeOf(l));

          { compress and store the file temporary}
          tmpFile := TFileStream.Create('tmp',fmCreate);

          compr := TZCompressionStream.Create(tmpFile, zcMax);
          try
            compr.CopyFrom(infile,l);
          finally
            compr.Free;
            tmpFile.Free;
          end;

          { append the compressed file to the destination file }
          tmpFile := TFileStream.Create('tmp',fmOpenRead);
          try
            outfile.CopyFrom(tmpFile,0);
          finally
            tmpFile.Free;
          end;
        finally
          infile.Free;
        end;
      end;
    finally
      outfile.Free;
    end;
    DeleteFile('tmp');
  end;
end;


procedure DecompressFiles(const Filename, DestDirectory : String);
var
 dest,s : String;
 decompr : TZDecompressionStream;
 infile, outfile : TFilestream;
 i,l,c : Integer;
begin
  // IncludeTrailingPathDelimiter (D6/D7 only)
  dest := IncludeTrailingPathDelimiter(DestDirectory);

  infile := TFileStream.Create(Filename,fmOpenRead);
  try
    { number of files }
     infile.Read(c,SizeOf(c));
     for i := 1 to c do begin
       { read filename }
       infile.Read(l,SizeOf(l));
       SetLength(s,l);
       infile.Read(s[1],l);

       { read filesize }
       infile.Read(l,SizeOf(l));

       { decompress the files and store it }
       s := dest+s; //include the path

       outfile := TFileStream.Create(s,fmCreate);

       decompr := TZDecompressionStream.Create(infile);
       try
         outfile.CopyFrom(decompr,l);
       finally
         outfile.Free;
         decompr.Free;
       end;
     end;
   finally
     infile.Free;
   end;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  CompressFiles(Memo1.Lines,'dest.myzip');
end;

procedure TForm1.Button2Click(Sender: TObject);
begin
  DecompressFiles('dest.myzip','C\');
end;