  We present an experimental study of the turn-on delay in pulsed mid-infrared
quantum cascade lasers. We report the unexpectedly long delay time depending on
the pumping current, which does not agree with conventional theoretical
predictions for step-like excitation. Similar behavior has been observed in
InP- and InAs-based QCLs emitting near 8${\mu}$m. Numerical simulations
performed using a model based on rate equations for excitation by current
pulses with non-zero rise time provide fair agreement with our observations.
