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

Reduced Dynamics from the Unitary Group to Some Flag Manifolds : Interacting Matrix Riccati Equations