In the following we discuss two models of ecological- or biological-like evolution. First, a simple dynamical model studied through Monte Carlo simulations and describing the gradual evolution of species, is mainly emphasized: there are two independent competing mechanisms for evolution or growth, i.e. two for removing a species from the system, and one for creating a new species. Regardless of the initial concentration of species,the system always reaches the same final state, characterized by the same concentration and the same average adaptation. The system is finally not homogeneous and contains species with different values of the adaptation. The evolution does not show avalanches, nor punctuated equilibria, but leads to an organized state. The behavior seems to have been found in evolving biological systems. The next simple dynamical model is based on the Bak-Sneppen model, but with a variable number of species as done by Vandewalle and Ausloos in 1996, allowing for branching, death of ancestor, and “interaction” between the new species at finite or infinite range. The system evolution shows avalanches, punctuated equilibria, and screening of evolution within an organized state. The geometrical, biological and physical critical exponents are numerically determined and lead to simple relations among them. ©1999 American Institute of Physics.