We have considered radiationless decay in a simple skeleton spectrum of states between which there are systematic functional and random coupling matrix elements; the former are treated as a perturbation of the latter. As particular examples we have analyzed mixing of constant coupling and random coupling and mixing of Lorentzian coupling and random coupling in a spectrum which can model photodissociation and/or vibrational relaxation, and have calculated the total dissociation probability and lifetime of the initially excited state. For small times the constant coupling-random coupling case leads to a linear combination of t and t2 terms characteristic of nonsequential and sequential decays, respectively. The Lorentzian coupling-random coupling case can be thought of as a model for vibrational relaxation in solution. The calculated time evolution of the population of the initially excited vibrational mode exhibits two time constants for small times and is rather complex for larger times. The shorter time constant corresponds to the redistribution of energy among modes which are nearly resonant with the initially excited mode and the longer time constant corresponds to the relaxation to lower lying modes by the solvent. This is in good qualitative agreement with the experimental results of raiser et al.