In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the computational burden. Building blocks in the diagnostic measures are computed via the observations generated by the MH algorithm. Results from a simulation study and an illustrative real example are presented.