The next code shows how detect If my Delphi application is running under a 64-bit version of Windows.

uses 
  Windows;

    function IsWow64Process: Boolean;
    type
      TIsWow64Process = function( hProcess: Windows.THandle; var Wow64Process: Windows.BOOL): Windows.BOOL; stdcall;
    var
      IsWow64Process: TIsWow64Process;
      Wow64Process  : Windows.BOOL;
    begin
      Result := False;
      IsWow64Process := GetProcAddress(GetModuleHandle(Windows.kernel32), 'IsWow64Process');
      if Assigned(IsWow64Process) then
      begin
        if not IsWow64Process(GetCurrentProcess, Wow64Process) then
        Raise Exception.Create('Invalid handle');
        Result := Wow64Process;
      end;
    end;