Kinetic roughening with anysotropic growth rules

11 pages, 21 figures. submitted to PREInspired by the chemical etching processes, where experiments show that growth rates depending on the local environment might play a fundamental role in determining the properties of the etched surfaces, we study here a model for kinetic roughening which includes explicitly an anisotropic effect in the growth rules. Our model introduces a dependence of the growth rules on the local environment conditions, i.e. on the local curvature of the surface. Variables with different local curvatures of the surface, in fact, present different quenched disorder and a parameter $p$ (which could represent different experimental conditions) is introduced to account for different time scales for the different classes of variables. We show that the introduction of this {\em time scale separation} in the model leads to a cross-over effect on the roughness properties. This effect could explain the scattering in the experimental measurements available in the literature. The interplay between anisotropy and the cross-over effect and the dependence of critical properties on parameter $p$ is investigated as well as the relationship with the known universality classes