System for displaying a notification window from completely transparent to intermediate level of opacity as a function of time to indicate an event has occurred

A method and apparatus for notifying a computer user of the occurrence of an event are provided. An indication is received that an event has occurred. In response to receiving the indication, a notification window is gradually displayed by varying the opacity of the window. When the event comprises the receipt of a new electronic mail message, the notification window includes a notification message indicating that the new electronic mail message has been received. If a predetermined period of time elapses without a selection of the new message notification window being received, the window is gradually removed. The new message notification window may be displayed above the displays provided by other executing applications.