The effect of power-law aging on a contact process is studied by simulation
and using a mean-held approach. The introduced type of aging accounts for,
e.g., the growth of the virus fitness (HIV infection). We find that the sy
stem may approach its stationary state in a nontrivial, nonmonotonous way.
For the particular value of the aging exponent alpha =1 we observe a rich s
et of behaviors: depending on the process parameters, the relaxation to the
stationary state proceeds as 1/ln t or via a power law with a nonuniversal
exponent. Simulation results suggest that for 0<<alpha><1, the absorbing-s
tate phase transition is in the universality class of directed percolation.