  In this paper we study a nonlinear size-structured population model with
distributed delay in the recruitment. The delayed problem is reduced into an
abstract initial value problem of an ordinary differential equation in the
Banach space by using the delay semigroup techniques. The local existence and
uniqueness of solution as well as the continuous dependence on initial
conditions are obtained by using the general theory of quasi-linear evolution
equations in nonreflexive Banach spaces, while the global existence of solution
is obtained by the estimates of the solution and the extension theorem.
