The Fuchs-Nordheim model is extended to develop an approximate solution for reactor excursion analysis that includes delayed neutrons and nonadiabatic systems. Division of the time domain allows a superposition of the prompt burst power as predicted by the Fuchs-Nordheim solution and the delayed-neutron tail power. The solutions are applicable to reactor excursions of $1.00 or above up to the time the physical or nuclear dynamic properties are changed (such as by moderator expulsion or core meltdown) or when space-time effects dominate. Time-dependent relations are obtained for both reactor power and energy generated. The initial delayed-neutron-tail power is shown to be nearly independent of pulse size. Experimental time-dependent measurements of TRIGA pulses from $1.00 to $3.21 are reported and compared; peak power and energy generated to peak power are provided. Time-dependent excursion data for the HPPR and TREAT reactors are also compared with predictions of this theory. Theoretical results are provided with figures of reactor power and total energy generated for application to excursions with minimum periods from 0.002 to 1.0 sec for reactor systems with 233U, 235U, and 239Pu fuels.