  We introduce a novel local time-stepping technique for marching-in-time
algorithms. The technique is denoted as Causal-Path Local Time-Stepping (CPLTS)
and it is applied for two time integration techniques: fourth order
low--storage explicit Runge--Kutta (LSERK4) and second order Leapfrog (LF2).
The CPLTS method is applied to evolve Maxwell's curl equations using a
Discontinuous Galerkin (DG) scheme for the spatial discretization. Numerical
results for LF2 and LSERK4 are compared with analytical solutions and the
Montseny's LF2 technique. The results show that the CPLTS technique improves
the dispersive and dissipative properties of LF2-LTS scheme.
