[Страдалецъ]

Так попробуйте:

Код:

procedure TForm1.Button1Click(Sender: TObject);
var
BeginDate, EndDate, WrkDate: TDate;
r: integer;

begin
for r:= 0 to StringGrid1.RowCount-2 do
begin
if (stringgrid1.Cells[0, r] <> '') and (stringgrid1.Cells[1, r] <> '') and (stringgrid1.Cells[0, r+1] <> '')
then begin
       BeginDate := StrToDate(Stringgrid1.Cells[0, r]);
       EndDate := StrToDate(Stringgrid1.Cells[1, r]);
       WrkDate := StrToDate(Stringgrid1.Cells[0, r+1]);
       if (WrkDate > BeginDate) and (WrkDate < EndDate) then
  showmessage(StringGrid1.Cells[0,r+1] + ' входит в период ' + ' от '+ DateToStr(BeginDate) + ' по ' + DateToStr(EndDate));
end;
end;
end;