Summary: In the induction of relational concepts and productions from examples and counterexamples, a ‘counterfactual’ is a set of conditions which must be false if a generalization is to be satisfied. Multilevel counterfactuals may themselves contain counterfactuals nested to any level, providing a series-like concept representation mechanism. An algorithm is presented, with correctness proof, which computes multilevel counterfactuals by recursively reducing the original induction problem to a smaller ‘residual’ problem, whose generalization gives the desired counterfactual. Winston’s empirical method for determining ‘must-not’ conditions (single level counterfactuals) is shown to yield erroneous results in certain rather ordinary circumstances. Computed examples are presented for the generalization of complex geometric scenes and the learning of blocksworld operators without resorting to the common CLEARTOP expedient.