Security challenges for Cloud or Fog-based machine learning services pose several concerns. Securing the underlying Cloud or Fog services is essential, as successful attacks against these services, on which machine learning applications rely, can lead to significant impairments of these applications. Because the requirements for AI applications can also be different, we differentiate according to whether they are used in the Cloud or in a Fog Computing network. This then also results in different threats or attack possibilities. For Cloud platforms, the responsibility for security can be divided between different parties. Security deficiencies at a lower level can have a direct impact on the higher level where user data is stored. While responsibilities are simpler for Fog Computing networks, by moving services to the edge of the network, we have to secure them against physical access to the devices. We conclude by outlining specific information security requirements for AI applications.