Delphi: Function keys like F1, F2 and F3 do not work in FormKeyDown event

In the FormKeyDown event, I want to react to the function keys (F1, F2, F3, F4, F5, F6, F7, F8, F9, F10, F11 and F12) and assign an appropriate action (HotKey). For this I use the following code:

procedure TForm1.FormKeyDown(Sender: TObject; var Key: Word;
  Shift: TShiftState);
begin
  if Key = VK_F1 then Function1();
  if Key = VK_F2 then Function2();
  if Key = VK_F3 then Function3();
  //usw
end;

Problem: For some reason, it does not work. Apparently, when pressing F1, not even the FormKeyDown event of the form is called! What am I doing wrong? I have checked the code for many times and with all other Virtual Keys such as VK_SPACE, it works perfectly! Only with the function keys there is a problem!