  We consider a class of generalized Kuznetsov--Zabolotskaya--Khokhlov (gKZK)
equations and determine its equivalence group, which is then used to give a
complete symmetry classification of this class. The infinite-dimensional
symmetry is used to reduce such equations to (1+1)-dimensional PDEs. Special
attention is paid to group-theoretical properties of a class of generalized
dispersionless KP (gdKP) or Zabolotskaya--Khokhlov equations as a subclass of
gKZK equations. The conditions are determined under which a gdKP equation is
invariant under a Lie algebra containing the Virasoro algebra as a subalgebra.
This occurs if and only if this equation is completely integrable. A similar
connection is shown to hold for generalized KP equations.
