Summary: A new model for the growth of a single-species with a two-stage structure is developed employing a state-dependent age of maturity. The paper discusses some remarks in a previous model where the time to maturity is state dependent. Then, we present a new model which is mainly based on making the maturation period of juveniles depend on the total population size not at the present time \(t\) but at an earlier time stage, namely, the time when they were born. The paper considers both biological and mathematical aspects. Emphasis is given to the basic theory of the solutions, such as local and global properties of existence, uniqueness, positivity and boundedness.