The problem of state observation for nonlinear systems in which the output measurement is accessible after some time delay is studied in this paper, and an observer is proposed for the unforced case. On this matter no results, to our knowledge, are available in literature. The proposed observer is a nonlinear delay system and is an identity observer, in that it reproduces exactly the system equation when initialized by the true initial state. Its implementation is easy and computer simulations show its effectiveness. When the delay is equal to zero, this algorithm is equal to the one for nonlinear systems in [9]. Sufficient conditions are obtained that ensure convergence to zero of the observation error for any output delay.