This article presents new results for the automated verification of automata communicating asynchronously via FIFO or bag buffers. The analysis of such systems is possible by comparing bounded asynchronous compositions using equivalence checking. When the composition exhibits the same behavior for a specific buffer bound, the behavior remains the same for larger bounds. This enables one to check temporal properties on the system for that bound and this ensures that the system will preserve them whatever larger bounds are used for buffers. In this article, we present several decidability results and a semi-algorithm for this problem considering FIFO and bag buffers, respectively, as communication model. We also study various equivalence notions used for comparing the bounded asynchronous systems.