The paper describes the formulation and implementation of the broadband finite element time domain algorithm. The presented formalism is valid to analysis of electromagnetic phenomena in linear, frequency selective materials. The complex profile of permittivity of materials is approximated using a set of the Lorentz resonance models. The solution of the integro-differential second order equation is obtained using a singlestep integration scheme and a recursive convolution algorithm. The discussed formulation enables to adopt the structure of the narrowband part as well as the phase of calculation of the convolution equations for the subsequent components. The properties of the algorithm are validated using a finite difference broadband algorithm.