The problems for both services began shortly after 5am Wednesday morning but was back online just after 10am AEST.
iMessage is an instant messaging service and Facetime is a video calling service.
Apple posted a short notice on its website saying “some users” were unable to make calls or send messages but provided no additional information.
It was unclear how widespread is the outage, but Twitter is seeing tens of messages every minute from users who say they are affected by the problem.
Of the two services, Facetime is the older, having been introduced with the iPhone 4 in 2010. IMessage was introduced a year later when Apple released iOS 5.
Martyn Williams covers mobile telecoms, Silicon Valley and general technology breaking news for The IDG News Service. Follow Martyn on Twitter at @martyn_williams. Martyn’s e-mail address is firstname.lastname@example.org