Efficient Time-Domain techniques based on the Method of Moments are presented in this paper at the aim to predict the electromagnetic responses of a communication system while invoking the coupling between these components. This system is composed of a rectangular cavity containing an interior scatterer coupled to an external scatterer through a slot mounted on a cavity wall. In order to make the problem mathematically tractable, Time-Domain Electric Field Integral Equations based on the equivalence principle and the boundary conditions are developed. Thus, the Method of Moments is applied in space and time-domains to solve the equation system. In time-domain, the temporal part of the unknown coefficients is expressed as linear combination of: the Laguerre functions in the first solution and the B-Spline functions in the second one. The transient responses of the system are obtained by the two proposed techniques. In the light of the comparison results, the Laguerre functions are shown to be the more accurate. Based on these functions, a coupling study between the components of the proposed system is conducted.