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uses zlib;

procedure CompressStream(inpStream, outStream: TStream);
var
  InpBuf, OutBuf: Pointer;
  InpBytes, OutBytes: Integer;
begin
  InpBuf := nil;
  OutBuf := nil;
  try
    GetMem(InpBuf, inpStream.Size);
    inpStream.Position := 0;
    InpBytes := inpStream.Read(InpBuf^, inpStream.Size);
    CompressBuf(InpBuf, InpBytes, OutBuf, OutBytes);
    outStream.Write(OutBuf^, OutBytes);
  finally
    if InpBuf <> nil then FreeMem(InpBuf);
    if OutBuf <> nil then FreeMem(OutBuf);
  end;
end;

procedure DecompressStream(inpStream, outStream: TStream);
var
  InpBuf, OutBuf: Pointer;
  OutBytes, sz: Integer;
begin
  InpBuf := nil;
  OutBuf := nil;
  sz     := inpStream.Size - inpStream.Position;
  if sz > 0 then
    try
      GetMem(InpBuf, sz);
      inpStream.Read(InpBuf^, sz);
      DecompressBuf(InpBuf, sz, 0, OutBuf, OutBytes);
      outStream.Write(OutBuf^, OutBytes);
    finally
      if InpBuf <> nil then FreeMem(InpBuf);
      if OutBuf <> nil then FreeMem(OutBuf);
    end;
  outStream.Position := 0;
end;

procedure savememoryliste(liste:tstringlist;const dateiname:string);
var ms1, ms2: TMemoryStream;
begin
  ms1 := TMemoryStream.Create;
  try
    ms2 := TMemoryStream.Create;
    try
      liste.SaveToStream(ms1);
      CompressStream(ms1, ms2);
      ms2.SaveToFile(dateiname);
    finally
      ms2.Free;
    end;
  finally
    ms1.Free;
  end;
end;

procedure loadmemoryliste(liste:tstringlist;const dateiname:string);
var
  ms1, ms2: TMemoryStream;
begin
  ms1 := TMemoryStream.Create;
  try
    ms2 := TMemoryStream.Create;
    try
      ms1.LoadFromFile(dateiname);
      DecompressStream(ms1, ms2);
      liste.LoadFromStream(ms2);
    finally
      ms2.Free;
    end;
  finally
    ms1.Free;
  end;
end;                    

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uses rc4;

procedure TForm1.WriteBtnClick(Sender: TObject);
var ListboxStream: TMemoryStream;
    RC4Writer: TRC4StreamWriter;
begin
  ListboxStream:=TMemoryStream.Create;
  try
    ListBox1.Items.SaveToStream(ListboxStream);
    ShowMessage(IntToStr(ListboxStream.Size));  // funktioniert
    // es wird auch noch eine leere Datei erzeugt
    RC4Writer := TRC4StreamWriter.Create(TFileStream.Create('ausgabe.txt', fmCreate or fmShareDenyWrite), 'geheim');
    try
      // Hier kommt der Fehler
      // ... ist eine Exception der Klasse EReadError aufgetreten.
      // Meldung: 'Stream-Lesefehler'.
      RC4Writer.CopyFrom(ListboxStream, ListboxStream.Size);      
    finally
      RC4Writer.Free;
    end;
  finally
    ListboxStream.Free;
  end;
end;                    

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  ListboxStream:=TMemoryStream.Create;
  try
    ListBox1.Items.SaveToStream(ListboxStream);
    ListboxStream.Position := 0; // Stream wieder auf Anfang
    ShowMessage(IntToStr(ListboxStream.Size));  // funktioniert
    ...