Anticipatory Classifier Systems (ACS) are classifier systems that learn by using the cognitive mechanism of anticipatory behavioral control which was introduced in cognitive psychology by Hoffmann [4]. They can learn in deterministic multi-step environments.¹ A stepwise introduction to ACS is given. We start with the basic algorithm and apply it in simple “woods” environments. It will be shown that this algorithm can only learn in a special kind of deterministic multi-step environments. Two extensions are discussed. The first one enables an ACS to learn in any deterministic multi-step environment. The second one allows an ACS to deal with a special kind of non-Markov state.