We have investigated the time evolution of (Renyi) entanglement entropies for a locally excited state defined by acting with a local operator. When the subsystem is given by a half of the total space, we have found that they approach finite constants in free field theories or solvable models. On the other hand, those entropies in holographic field theories logarithmically increase with t even at the late time. Thus they are expected to be a candidate which reveals the characteristic feature of holographic field theories. In the current works, we found that the entropies in free field theories are given by the probability with which the quasi-particle created by local operators located in the subsystem. We also introduce a toy model where a particle created by a local operator freely propagates. By using this model, we can reproduce the result which is obtained by the replica trick. I would like to explain the detail of our results as long as permitted.