Anisotropy and non-universality in kinetic roughening

We introduce a new model for kinetic roughening which exhibits a non-universal behavior for the roughness exponent, in agreement with many experimental findings. The model, inspired by the chemical etching processes, takes explicitly into account the effect of anisotropy, say the dependence of the growth rule on the local environment conditions. The interplay between anisotropy and non-universality is investigated as well as the relationship with the known universality classes.