The invention concerns a process for preparing compounds of general formula (I) ##STR1##

wherein R and R represent an alkyl radical or an aryl group; and R" is hydrogen or a CO—R¹ group wherein R¹ is an alkyl radical or an aryl group; and wherein these compounds are or not in the thiazolidine form; by protecting the N-acyl-L-cysteine to form an intermediate compound; and then by coupling said intermediate compound with S-acylcysteamine hydrochloride or with thiazolidine.