Results associated with Neumann-type economic growth models are described. We present a new generalization of the Neumann model with the idea of explaining and unifying certain basic results obtained by M. Morishima and J. Łos in proving general existence theorems. The idea of replacing constant input and output matrices in the Neumann model by those which depend continuously on the growth rate and on the price vector suggested and developed by {\it M. Morishima} [”Equilibrium stability and growth” (1964;

Zbl 0117.154)], is coupled with an asymmetric-type generalization of the original Neumann model, developed by {\it J. Łos} [in: Computing Equilibria: How and Why, Proc. Int. Conf., Torun 1974, 141-157 (1976;

Zbl 0364.90024)]. Consequently, many of our results resemble and partly replace those obtained in both model generalizations.