  In one complex variable it is well known that if we consider the family of
all holomorphic functions on the unit disc that fix the origin and with first
derivative equal to 1 at the origin, then there exists a constant $\rho$,
independent of the functions, such that in the image of the unit disc of any of
the functions of the family there is a disc of universal radius $\rho.$ This is
the so celebrated Landau's theorem. Many counterexamples to an analogous result
in several complex variables exist. In this paper we introduce a class of
holomorphic maps for which one can get a Landau's theorem and a Brody-Zalcman
theorem in several complex variables.
