We present a method for providing response-time guarantees in Asynchronous Transfer Mode (ATM) networks. The method is based on traditional real-time CPU Response-Time Analysis (RTA), and is intended to be used for admission control of hard real-time traffic. The method determines if a new connection can be admitted without violating the strict timing requirements specified for the new as well as old connections. We illustrate the merits of our method by comparing it with Weighted Fair Queuing (WFQ) and the Calculus for Network Delays (CND). Two types of comparisons are made. In the first, we evaluate how well the associated analysis can accommodate different traffic scenarios and loads, and in the second comparison we use simulation to compare observed worst-case behaviors with estimates obtained by the analysis. The comparisons clearly indicate that RTA outperforms both WFQ and CND for a set of realistic traffic scenarios.