  We show theoretically and experimentally that a quantum cascade laser (QCL)
in an external Fabry-Perot cavity (EC) can produce regular self-pulsations (SP)
of the output intensity at frequencies ~75 GHz. We recognize that the
propagation delay in EC provides QCL with a "memory" mechanism to preserve the
regularity and coherence of the pulse train on the intervals significantly
exceeding the sub-picosecond gain coherence and gain recovery times. These
results may point to novel practical approaches for producing regular
time-domain SPs and pulse trains in the Mid-IR QCLs. Otherwise, due to a
multimode Risken-Nummedal-Graham-Haken (RNGH) instability, free-running FP QCLs
exhibit SPs at Rabi flopping frequencies in the THz range, which in addition,
reveal a quasi-periodic chaotic behavior if the cavity round trip time is a few
picoseconds or more.
