We address cases of flows submitted to the Coriolis force, such as geophysical flows at mesoscales, whether they be atmospheric or oceanographic, or industrial flows in rotating devices, such as turbomachinery. Our goal is to improve the modelling of these flows from the point of view of the anisotropy which develops therein. Therefore, we discard the effects of boundaries and treat homogeneous turbulence equations in Fourier space. We derive a wave-turbulence model for rapidly rotating turbulent flows. This Asymptotic Quasi-Normal Markovian (AQNM) model is valid in the limit of small Rossby number and high Reynolds number. Previous works in this field have been done by Benney & Saffman and more recently by Galtier for modelling inertial wave turbulence, in which the dispersion relation of the waves is more complex than that considered by Zakharov et al.. Our model of rotating turbulence locates itself between purely linear theories such as RDT and EDQNM-type models which where adapted for including inertial waves, although remaining fully nonlinear models. Unlike AQNM, these EDQNM3 models deal with the entire Fourier space, and compare very well with Direct Numerical Simulations.