Addition salts of cysteamine with acids are prepared by reacting aziridine with an organic sulfur compound of oxidation state -2 and with a ketone and then subjecting the thiazolidine formed as an intermediate to acid hydrolysis, by a process in which aziridine and the ketone are reacted with ammonium hydrogen sulfide or with a metal hydrogen sulfide with the addition of a moderately strong or strong acid at from -10.degree. to +100.degree. C. and a pH which is greater than or equal to 8.5 is maintained.