The PlayStation Store Twitter feed said Friday that some users were having trouble logging into its network. It said engineers were investigating.
A notice on Microsoft's Xbox website said it knew some users were having trouble signing in. it said, "We're aware of this issue, and we're working to find a fix ASAP!"
The problems were affecting Xbox Live Core Services, though most other applications were up and running, it said.
Earlier this month the PlayStation store also experienced spells of inaccessibility. That followed a cyberattack on computer systems of Sony Pictures Entertainment that led to the release of confidential information on the Internet.
A hacker group calling itself Lizard Squad appeared to take responsibility for the disruptions on its Twitter account.