  In this paper we treat the time evolution of unitary elements in the N level
system and consider the reduced dynamics from the unitary group U(N) to flag
manifolds of the second type (in our terminology). Then we derive a set of
differential equations of matrix Riccati types interacting with one another and
present an important problem on a nonlinear superposition formula that the
Riccati equation satisfies.
  Our result is a natural generalization of the paper {\bf Chaturvedi et al}
(arXiv : 0706.0964 [quant-ph]).
