  Systems of nonlinear ordinary differential equations are constructed, for
which the general solution is algebraically expressed in terms of a finite
number of particular solutions. Expressions of that type are called the
nonlinear superposition formulas. These systems are connected with local Lie
groups tranformations on their homogeneous spaces. In the presented work the
nonlinear superposition formulas are constructed for the case of the SO(3,2)
group and some aspects in the general case of SO(n+1,n) are studied.
