In this article we address the problem of distinguishing between two different geodynamical histories using a geometrical description of the fault system in the Ethiopian Rift. The regional distribution of structures has been characterized by the estimation of the generalized fractal dimensions for the whole system as well as for the subsets of faults oriented along two different directions, using the importance sampling approach. Results show that the two subsets are monofractal with different dimensions, providing an independent indication that different dynamical processes have been responsible for the fault generation of this area. ¿ 1999 American Geophysical Union