Associative neural memory of Hopfield type with a restricted amount of connections (Cellular-Neuron Associative Memory - CNAM) is investigated. Algorithms for CNAM designing take most advantage of the fine-grained parallelism induced both by cell operational independence and by connection locality. A very important property is also the fact that learning and retrieval processes may be performed in the same cellular array. Some necessary and sufficient conditions of strong stability and k-attractability are obtained, which are expressed in terms of cell neighborhood relations of stored patterns. Simulation of learning and retrieval processes in a CMAM storing symbols drawn in thin lines showed the following: for this class of patterns it is possible to provide strong stability approximately for 21&l prototypes where Q is the cardinility of neuron neighborhood, with the capability of restoring 60 - 70 % of l-distortions.