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The Markov dynamics of an infinite continuum birth-and-death system of point particles with age is studied. Each particle is characterized by its location $x\in {ℝ}^d$ and age $a_x\ge 0$. The birth and death rates of a particle are age dependent. The states of the system are described in terms of probability measures on the corresponding configuration space. The exact solution of the  evolution equation for the correlation functions of first and second orders is found.