K e y w o r d s : scatter, gather, collective comnmnication, asynchronous communication model, communication tree. AbstractCollective communication such as scatter, gather, broadcast, and total exchange plays an important role on the performance of parallel and distributed processing. So far, several parallel collective communication algorithms have been studied in synchronous comnmnication models, but it is necessary to design and anMyze parallel algorithms using a more realistic communication model. This paper introduces an asynchronous communication model between processors, and evaluates the execution time of operations which include scatter, gather and some computations for data initially located at one processor. The results show that the execution time in sending data in a single direction is less than that of dual directions for asynchronous communication. This paper also introduces the logarithmic correction of the bisection communication tree, and evaluates the communication time of several instances. O We can also compare the first multi-communication method with the sequential c omnmnication operation. T h e o r e m 2 In the asynchronous communication model, let T,~eq be the execution time of the sequential communication operation for p processors. Let T,,,,~ also be the execution time of the multicommunication operation using Method 1. Then there are at most three real solutions for T~q = T,,r~i in the case that tisena = tlrecv, C > 0, p ~ 2 and T~,,,