Some nonlinear approximants, i.e., exponential-sum interpolation with equal distance or at origin, (0,1)-type, (0,2)-type and (1,2)-type fraction-sum approximations, for matrixvalued functions are introduced. All these approximation problems lead to a same form system of nonlinear equations. Solving methods for the nonlinear system are discussed.Conclusions on uniqueness and convergence of the approximants for certain class of functions are given.