A unified approach is presented for the design of two classes of nonminimum phase transfer functions providing an optimum Cheby̅shev passband magnitude response and approximating to a constant delay over the larger part of the passband in terms of a mini-max norm. In one of these classes, the numerator polynomial of the transfer function is of even degree, since all its zeros possess quadrantal symmetry, or are located in pairs symmetrically about the origin. The other class, based on pole-zero cancellation in the left half of the complex frequency plane, offers more flexibility in practical design by permitting the passband magnitude ripple and the delay error (or the delay bandwidth) to be specified independently. In addition, the latter yields, in many practical applications, a more economical solution from the point of view of both the complexity of the realised network and the ease of tuning, as demonstrated by some suitably chosen examples.