We associate to an arbitrary Z-gradation of the Lie algebra of a Lie group
a system of Riccati-type first order differential equations. The particular
cases under consideration are the ordinary Riccati and the matrix Riccati
equations. The multidimensional extension of these equations is given. The
generalisation of the associated Redheffer-Reid differential systems appear
s in a natural way. The connection between the Toda systems and the Riccati
-type equations in lower and higher dimensions is established. Within this
context the integrability problem for those equations is studied. As an ill
ustration, some examples of the integrable multidimensional Riccati-type eq
uations related to the maximally nonabelian Toda systems are given.