Given an open bounded convex subset $\omega$ of $R^p$, a strictly elliptic differential operator $L$ and a continuous function $\lambda:\bar\Omega \to[1,0]$, and denoted with $T_L$ the Dirichlet operator associated with $L$, the Lototsky-Schnabl operators associated with $T_L$ and $\lambda$ are investigated. In particular, conditions are established which ensure the existence of a Feller semigroup represented by limit of powers of these operators. Then the analytic expression of the infinitesimal generator is determined and some properties of the semigroup are deduced. Finally, the saturation class of Lototsky-Schnabl operators is determined.