In this paper we consider three variants of accepting networks of evolutionary processors. It is known that two of them are equivalent to Turing machines. We propose here a direct simulation of one device by the other. Each computational step in one model is simulated in a constant number of computational steps in the other one while a Florin Manea is on leave of absence from the University of Bucharest. P. Bottoni Á A. Labella Department of Computer Science, ‘‘Sapienza’’ University of Rome, Via Salaria 113, 00198 Rome, Italy