Machine recognition of partially occluded objects is essential for any realistic automatic object recognition (AOR) system. This important problem however, has been mostly ignored by the researchers and developers of AOR systems. Due to this lack of attention very little work is done even in the formulation of the problem and much less for its solution. In this paper I attempt to analyze the occlusion problem, define its various categories, and to present an approach for its solution in some of these categories. I also present some of the empirical results of the implementation of the approach on real imagery. These results have been very encouraging so far. However, more work is definitely needed to be done for the resolution of this problem.