Jordan and left derivations on locally $C{*}$-algebras

We show that left derivations as well as Jordan derivations on locally $C^{*}$-algebras are always continuous. We also obtain some noncommutative extensions of the classical Singer-Wermer theorem for locally $C^{*}$-algebras: (1) Every left derivation $D$ on a locally $C^{*}$-algebra $A$ is identically zero. (2) Every Jordan derivation $D$ on a locally $C^{*}$-algebra $A$ which satisfies $[D(x),x]D(x)=0$ for all $x$ in $A$, is identically zero.