  The so called generalized down-up algebras are revisited from a viewpoint of
Gr\"obner basis theory. Particularly it is shown explicitly that generalized
down-up algebras are solvable polynomial algebras (provided $\lambda\omega\ne
0$), and by means of homogeneous Gr\"obner defining relations, the associated
graded structures of generalized down-up algebras, namely the associated graded
algebras, Rees algebras, and the homogenized algebras of generalized down-up
algebras, are explored comprehensively.
