The Problem of allpass filter design for phase approximation and equalization in the Chebyshev sense is solved by using a generalized Remez algorithm. Convergence to the unique optimum is guaranteed and is achieved rapidly in the actual implementation. The well-known numerical problems for higher degree filters are analyzed and solved by a simple approach. Possible applications are: design of filters with a desired phase response (e.g., a delay element), the design of phase equalizers, or the design of recursive filters with magnitude prescriptions using parallel allpass filters. For the latter the algorithm can be modified to allow arbitrary tolerance schemes for the magnitude response.