[NumLock]

TCriticalSection должна быть глобальной:

Код:

unit Unit1;

interface

uses
  SyncObjs,
  Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms,
  Dialogs, DB, DBTables, Grids, DBGrids, StdCtrls;

type
  TMyThread = class(TThread)
  private
    procedure Avatar;
  protected
    procedure Execute; override;
  public
    i: Integer;
    constructor Create;
  end;

  TForm1 = class(TForm)
    Memo1: TMemo;
    Button1: TButton;
    procedure Button1Click(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;
  cs: TCriticalSection;

implementation

{$R *.dfm}

{ TMyThread }

procedure TMyThread.Avatar;
begin
  Form1.Memo1.Lines.Add(IntToStr(i));
end;

constructor TMyThread.Create;
begin
  inherited Create(True);
  FreeOnTerminate:=True;
end;

procedure TMyThread.Execute;
begin
  cs.Acquire;
  try
    Sleep(i);
  finally
    cs.Release;
  end;
  Synchronize(Avatar);
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
  with TMyThread.Create do
  begin
    i:=2000;
    Resume;
    Sleep(100);
  end;
  with TMyThread.Create do
  begin
    i:=1000;
    Resume;
    Sleep(100);
  end;
  with TMyThread.Create do
  begin
    i:=500;
    Resume;
    Sleep(100);
  end;
end;

initialization
  cs:=TCriticalSection.Create;

finalization
  cs.Free;

end.