  Among systems that display generic scale invariance, those whose asymptotic
properties are anisotropic in space (strong anisotropy, SA) have received a
relatively smaller attention, specially in the context of kinetic roughening
for two-dimensional surfaces. This is in contrast with their experimental
ubiquity, e.g. in the context of thin film production by diverse techniques.
Based on exact results for integrable (linear) cases, here we formulate a SA
Ansatz that, albeit equivalent to existing ones borrowed from equilibrium
critical phenomena, is more naturally adapted to the type of observables that
are measured in experiments on the dynamics of thin films, such as one and
two-dimensional height structure factors. We test our Ansatz on a paradigmatic
nonlinear stochastic equation displaying strong anisotropy like the Hwa-Kardar
equation [Phys. Rev. Lett. 62, 1813 (1989)], that was initially proposed to
describe the interface dynamics of running sand piles. A very important role to
elucidate its SA properties is played by an accurate (Gaussian) approximation
through a non-local linear equation that shares the same asymptotic properties.
