In this paper, we propose two implementations of the SOFM on parallel computers. One is for a MIMD computer, the other one is for a SIMD computer. We propose a new learning method for the SOFM using a block strategy. This allows to exploit the high performance level of the new generation of parallel computers. We show that the block strategy performs well on several examples outperforming classical implementations. A model to describe the performance of this algorithm is proposed and compared with experimental data. Finally, we compare experimental results on the two classes of parallel computers.