In this paper, the authors have studied the notion of atomicity in message-passing distributed programs. The difference between the notion of atomicity in shared memory programs and message passing programs has been discussed in detail. Due to the nature of communication in messagepassing programs, the atomicity requirement in shared memory programs (serializability) does not guarantee the same level of atomicity in message-passing programs. They have referred to the atomicity level guaranteed by the serializability requirement in message-passing programs as the weak atomicity. They have defined the requirements that guarantee a level of atomicity in message-passing programs similar to that in shared memory programs.