The step-pulse response of a permeable and a radially nonuniformly conducting cylinder is obtained. Effects of the conductivity distribution pattern and the magnetic permeability on the transient response are examined in detail. It is found that: (i) the initial response (for t → 0) remains unaffected by both the inhomogeneity and the permeability of the cylinder; (ii) the large time response is governed only by the permeability; and (iii) the conductivity inhomogeneity is reflected only during intermediate times. Finally, the implications of the results for predicting the parameters of the cylinder are discussed.