In the time evolution of finite populations, the accumulation of harmf
ul mutations in further generations might lead to a temporal decay in
the mean fitness of the whole population that, after sufficient time,
would reduce population size and so lead to extinction. This joint act
ion of mutation load and population reduction is called Mutational Mel
tdown and is usually considered only to occur in small asexual or very
small sexual populations. However, the problem of extinction cannot b
e discussed in a proper way if one previously assumes the existence of
an equilibrium state, as initially discussed in this paper. By perfor
ming simulations in a genetically inspired model for time-changing pop
ulations, we show that mutational meltdown also occurs in large asexua
l populations and that the mean time to extinction is a nonmonotonic f
unction of the selection coefficient. The stochasticity of the extinct
ion process is also discussed. The extinction of small sexual N simila
r to 700 populations is shown and our results confirm the assumption t
hat the existence of recombination might be a powerful mechanism to av
oid extinction.