The aim of this talk is to present high-order numerical schemes for simulating the dynamics of systems of nonlinear Schr\"odinger/Gross-Pitaevskii equations. The usual high order numerical schemes based on time splitting technique can not be adapted for the computation of solutions to such equations in some situations. We introduce Runge-Kutta type schemes to obtain high order numerical schemes which can be used both for scalar and system of equations. We will consider exponential integrators such as exponential Runge--Kutta methods and Lawson methods, and high-order IMplicit-EXplicit (IMEX). We will show the properties of theses numerical schemes and develop a complete numerical study to investigate the properties of the schemes.