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uses TlHelp32;

function IsExeRunning(const AExeName: string): boolean;
var
  h: THandle;
  p: TProcessEntry32;
begin
  Result := False;

  p.dwSize := SizeOf(p);
  h := CreateToolHelp32Snapshot(TH32CS_SnapProcess, 0);
  try
    Process32First(h, p);
    repeat
      Result := AnsiUpperCase(AExeName) = AnsiUpperCase(p.szExeFile);
    until Result or (not Process32Next(h, p));
  finally
    CloseHandle(h);
  end;
end;					

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If IsExeRunning('explorer.exe') then //...