Function MyRemoveDir(sDir : String) : Boolean;
var
iIndex : Integer;
SearchRec : TSearchRec;
sFileName : String;
begin
Result := False;
sDir := sDir + '\*.*';
iIndex := FindFirst(sDir, faAnyFile, SearchRec);

while iIndex = 0 do begin
sFileName := ExtractFileDir(sDir)+'\'+SearchRec.Name;
if SearchRec.Attr = faDirectory then begin
if (SearchRec.Name <> '' ) and
(SearchRec.Name <> '.') and
(SearchRec.Name <> '..') then
MyRemoveDir(sFileName);
end else begin
if SearchRec.Attr <> faArchive then
FileSetAttr(sFileName, faArchive);
if NOT DeleteFile(sFileName) then
ShowMessage('Could NOT delete ' + sFileName);
end;
iIndex := FindNext(SearchRec);
end;

FindClose(SearchRec);

RemoveDir(ExtractFileDir(sDir));
Result := True;
end;

procedure TForm1.Button1Click(Sender: TObject);
begin
if MyRemoveDir('C:\2') then ShowMessage('Директория успешно удалена')
else ShowMessage('Не получается удалить директорию');
end;

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Завтра будет.Лучше.