Let $Y$ be a sequentially complete,locally convex linear-topological space,$(E,\Sigma ,\mu )$ a non-atomic measure space and $\varphi$ a real nondecreasing and continous for $u\geq 0$ function, equal to 0 for $u=0$.We prove the identity of the class of linear and pseudomodular continous operators from the Orlicz space $L_{\rho}^{*\varphi} (E,\Sigma ,\mu)$ into $Y$ with the class of similar operators from the Orlicz space $L_{\rho}^{*\overline{\varphi}} (E,\Sigma ,\mu)$ into $Y$, where $$\overline{\varphi}(u) =\int\limits_{0}^{u}p(t)dt \hs 4 true mm \operatorname{for} \hs 2 true mm u\geq 0 \hs 2 true mm \operatorname{and} \hs 2 true mm p(t)=\inf\limits_{t