What do you mean by "hangs".
Is it possible you are talking about a modal Dialog. If you open a modal dialog you can't do anything else in the applet until you close the dialog.
If you don't want a modal Dialog you can specify this in the Dialog constructor by setting modal to false.
From API:
Dialog
public Dialog(Frame owner,
String title,
boolean modal)
Constructs an initially invisible Dialog with the specified owner frame, title, and modality.
Parameters:
owner - the owner of the dialog
title - the title of the dialog. A null value will be accepted without causing a NullPointerException to be thrown.
modal - if true, dialog blocks input to other app windows when shown
Linda