This paper presents results obtained by applying two neural networks models Backpropagation (BP), and Self-Organized Feature Map (SOFM) to a new application of handwritten Arabic alphanumeric character (HAAC) recognition. A novel method for features extraction, based on a shadow projection is used. Both networks are trained using Arabic character samples written by different people (learning set). They are required, after the learning is over, to recognize characters out of the learning set. Evaluation of the recognition (classification) capability of the two models for 28 alphanumeric characters is achieved. Depending on the experimental results, a comparison of both algorithms is done.