Let $C(X)(C_{K}(X))$ denote the hyperspace of all nonempty closed connected subsets (subcontinua) of a locally compact Haus-dorff space X with the Fell topology. We prove that the following statements are equivalent: (1) X is locally connected. (2) C(X) is locally connected,. (3) C(X) is locally connected at each $E{in}C_{k}(X).(4) C_{k}(X)$ is locally connected.