On the basis of the maturity-time model of \textit{S. I. Rubinow} [Maturity- time representation for cell populations. Biophys. J. 8, 1055-1073 (1968)] which describes the cell densities of a growing cell population for the first few generation times in a good agreement to measurements, in this paper cell kinetic models for the growth of cell populations are developed which are able to reproduce also the long time (greater than about six mean generation times) growth properties of populations which tend to an equilibrium size after a few generation times. The location of a cell within the cell cycle is characterized by a biologically relevant maturity variable; the time rate of its change is the maturity velocity. The models utilize an initial distribution of maturity velocities over the cell population (which can be related to experimental results), and, different from Rubinow's approach, a nonconstant maturity velocity over the life time of the individual cells. For this, two mechanisms are considered; a time dependent rate of maturation for cells, and a maturity velocity which is a function of the total number of cells in the population. For the first version an exponential as well as an algebraic decaying maturity velocity is assumed. In the second model version a very general form of interaction between individual cells and the entire population leads also to an exponentially decaying maturity velocity for large times. All the model versions are uniformly valid for all times including the first few divisions, and agree remarkably well with appropriate Gompertz equations over a large time range giving a biologically plausible explanation for the empirical success of Gompertz equations in describing many cell division phenomena.