Effects of variation of the stimulus pulse shape on the excitation of a nonmyelinated nerve fibre were studied using a mathematical model based on the Hodgkin-Huxley equations. Efficiency of smoothly changing pulses was compared with that of rectangular pulses. For pulses shorter than the time to excitation, the rate of the stimulus rise did not determine the ability of a smoothly changing pulse to excite the fibre. For a given stimulus duration, the main factor was the pulse area or the charge delivered by the pulse. The strength-duration curve for smoothly changing pulses was a nonmonotonic function, in contrast to the curve for rectangular pulses. The dependence of latency on changes in the pulse area was non-linear. It would be nonmonotonic when the pulse area variation were due to the stimulus duration or the stimulus rise duration. More that one propagating intracellular action potential (IAP) could arise upon fibre activation by a long smoothly changing threshold stimulus. Upon activation of relatively short fibres the IAP could arise not at the site of the smoothly changing stimulus injection. The rectangular pulses of long duration were more efficient than the corresponding smoothly changing ones. Irrespective of the shape, the pulses whose duration at the foot is 1-2 ms, are more suitable for a prolonged threshold fibre activation.