  The differential and variational calculus on the $SL_{q}(2,R)$ group is
constructed. The spontaneous breaking symmetry in the WZNW model with
$SL_{q}(2,R)$ quantum group symmetry and in the $\sigma$-models with
${SL_{q}(2,R)/U_{h}(1)}$ ,$C_{q}(2|0)$ quantum group symmetry is considered.
The Lagrangian formalism over the quantum group manifolds is discussed. The
classical solution of $C_{q}(2|0)$ {$\sigma$}-model is obtained.
