The Finite-Difference Time-Domain (FDTD) method and Finite-Element (FEM) method are numerical techniques used for solving Maxwell's electromagnetic equations. FDTD-FEM hybrid methods opt for combining the advantages of both FDTD and FEM. In this dissertation, signal processing techniques were used to analyze the FDTD stability condition. A procedure, which reduces time-sampling error yet preserves the stability of algorithm is proposed. Both explicit and implicit time-stepping schemes were treated in the framework of the developed method. An improved version of the implicit-explicit FEM-FDTD hybrid method was developed. The new method minimizes reflection from the interface between different types of grids. A class of transfer functions with low reflection error for stable hybrid time-stepping was derived. The stability of the method is rigorously proven for a general three-dimensional case.