  The problem of the classification of the extensions of the Virasoro algebra
is discussed. It is shown that all $H$-reduced $\hat{\cal G}_{r}$-current
algebras belong to one of the following basic algebraic structures: local
quadratic $W$-algebras, rational $U$-algebras, nonlocal $V$-algebras, nonlocal
quadratic $WV$-algebras and rational nonlocal $UV$-algebras. The main new
features of the quantum $V$-algebras and their heighest weight representations
are demonstrated on the example of the quantum $V_{3}^{(1,1)}$-algebra.
