  We consider numerical solution of Coupled Nonlinear Schr\"{o}dinger Equation.
We prove stability and convergence in the $L_2$ space for an explicit scheme
which estimations is used for implicit scheme and compare both method. As a
test we compare numerical solutions of Manakov system with known analytical
solitonic solutions and as example of general system - evolution of two
impulses with different group velocity (model of pulses interaction in optic
fibers). Last example, a rectangular pulse evolution, shows asymptotic behavior
typical for Nonlinear Schr\"{o}dinger Equation asymptotics with the same
initial condition.
