In this paper we consider two nested computer codes, with the first code output as one of the second code inputs. A predictor of this nested code is obtained by coupling the Gaussian predictors of the two codes. This predictor is non Gaussian and computing its statistical moments can be cumbersome. Sequential designs aiming at improving the accuracy of the nested predictor are proposed. One of the criteria allows to choose which code to launch by taking into account the computational costs of the two codes. Finally, two adaptations of the non Gaussian predictor are proposed in order to compute the prediction mean and variance rapidly or exactly.