The quality of service (QoS) requirements are usually different from user to user in a multiaccess system, and it is necessary to take the different requirements into account when allocating the shared resources of the system. In this paper, we consider one QoS criterion--delay in a multiaccess system, and we combine information theory and queueing theory in an attempt to analyze whether a multiaccess system can meet the different delay requirements of users. For users with the same transmission power, we prove that only $N$ inequalities are necessary for the checking, and for users with different transmission powers, we provide a polynomial-time algorithm for such a decision. In cases where the system cannot satisfy the delay requirements of all users, we prove that as long as the sum power is larger than a threshold, there is always an approach to adjust the transmission power of each user to make the system delay feasible if power reallocation is available.