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In some applications, it is required to have continuous-time low-pass analog filtering systems which simultaneously possess a constant group delay in the passband and a narrow transition band. Usually, these systems are implemented by adding to the output of a filter with steep-amplitude selectivity (an elliptic filter, for instance) an all-pass filter which compensates the unfavorable run of the group delay response of the first filter. However, this compensation process will also increase the duration of the transient response of the resulting filtering system. This paper presents a new class of delay-compensated parameter-varying low-pass elliptic filters with a transient response of short duration. This improvement is achieved by means of a temporary change in the value of the filter parameters when a steplike transition with a minimum amplitude is detected in the input signal. As a consequence of the control strategy used to induce parameter variations in the proposed class of filters, its behavior is nonlinear in nature. Therefore, its stability properties (and particularly their bounded-input bounded-output stability) are also assessed. Simulations verifying the effectiveness of the new class of filters are presented and compared to the performance of delay-compensated and delay-uncompensated elliptic filters which were chosen as study cases.