One of the potential advantages of asynchronous circuits is that they can be optimized for average-case performance rather than worst-case performance. The performance analysis of asynchronous circuits, however, is more challenging than that of synchronous circuits because of the absence of a clock. We discuss some performance measures of special asynchronous networks, viz., response-time properties of asynchronous pipelines with various handshake communications. The response times of a pipeline are the delays between requests and succeeding acknowledgments for the first cell. We derive simple formulas for the bound on worst-case response time and average-case response time of such pipelines using a variable-delay model, where delays may vary between a lower and upper bound. The properties are independent of any particular implementation of the cells of the pipeline. The formulas give insight into the role of each parameter and allow a quick back-of-the-envelope prediction of the performance of an asynchronous pipeline.