  A Non-Markovian generalization of one-dimensional Contact Process (CP) is
being introduced in which every particle has an age and will be annihilated at
its maximum age $\tau$. There is an absorbing state phase transition which is
controlled by this parameter. The model can demonstrate oscillatory behavior in
its approach to the stationary state. These oscillations are also present in
the mean-field approximation which is a first-order differential equation with
time-delay. Studying dynamical critical exponents suggests that the model
belongs to the DP universlity class.
