uses
 RichEdit;
procedure TForm1.RichEdit1MouseMove(Sender: TObject; Shift: TShiftState;
 X, Y: Integer);
var
 iCharIndex, iLineIndex, iCharOffset, i, j: Integer;
 Pt: TPoint;
 s: string;
begin
 with TRichEdit(Sender) do
 begin
  Pt := Point(X, Y);
  // Get Character Index from word under the cursor
  iCharIndex := Perform(Messages.EM_CHARFROMPOS, 0, Integer(@Pt));
  if iCharIndex < 0 then Exit;
  // Get line Index
  iLineIndex := Perform(EM_EXLINEFROMCHAR, 0, iCharIndex);
  iCharOffset := iCharIndex - Perform(EM_LINEINDEX, iLineIndex, 0);
  if Lines.Count - 1 < iLineIndex then Exit;
  // store the current line in a variable
  s := Lines[iLineIndex];
  // Search the beginning of the word
  i := iCharOffset + 1;
  while (i > 0) and (s[i] <> ' ') do Dec(i);
  // Search the end of the word
  j := iCharOffset + 1;
  while (j <= Length(s)) and (s[j] <> ' ') do Inc(j);
  // Display Text under Cursor
  Caption := Copy(s, i, j - i);
 end;
end;