  Using renormalized field theory, we examine the dynamics of a growing
surface, driven by an obliquely incident particle beam. Its projection on the
reference (substrate) plane selects a ``parallel'' direction, so that the
evolution equation for the surface height becomes anisotropic. The phase
diagram of the model is controlled by the properties of an effective
anisotropic surface tension. Our renormalization group analysis suggests the
existence of a line of continuous transitions and a line of (potentially)
first-order transitions, which meet at a multicritical point. The full scaling
behavior for the continuous line and the multicritical point is discussed in
detail. Two novel universality classes for scale-invariant surface fluctuations
are found.
