If you have installed RxLib(http://www.rxlib.com/ with source), you can(It will run B.EXE while A.EXE is end.):
uses
RXShell;
{$R *.DFM}
procedure TForm1.Button1Click(Sender: TObject);
const
PathAExe=...;
PathBExe=...;
begin
if FileExecuteWait('A.EXE', '', PathAExe, esNormal)=-1 then
ShowMessage('Can not start A.EXE')
else
FileExecuteWait('B.EXE', '', PathBExe, esNormal);
end;