This paper presents a unified method for the delay analysis of a large class of random multiple - access algorithms. This method is based on a powerful theorem referring to regenerative processes, in conjunction with results from the theory of infinite dimensionality linear systems. The method is applied to analyze and compute the per packet expected delays induced by three algorithms, in the presence of the Poisson user model. The considered algorithms are: The controlled ALOHA algorithm, the 0.487 algorithm, and the n-ary stack algorithm. Additional keywords: Communications networks; Markovian models; Throughput; Delay. (Author).