for ii := 0 to Pred(IdMessage1.MessageParts.Count) do begin
if (IdMessage1.MessageParts.Items[ii] is TIdAttachmentFile) then begin
AuxString1 := TIdAttachmentFile(IdMessage1.MessageParts.Items[ii]).Filename;
...
f := TMemoryStream.Create;
TIdAttachmentFile(IdMessage1.MessageParts.Items[ii]).SaveToStream(f);
...
end
else
...
end;