This paper focuses on securely estimating the state of a nonlinear dynamical system from a set of corrupted measurements. In particular, we consider two broad classes of nonlinear systems, and propose a technique which enables us to perform secure state estimation for such nonlinear systems. We then provide guarantees on the achievable state estimation error against arbitrary corruptions, and analytically characterize the number of errors that can be perfectly corrected by a decoder. To illustrate how the proposed nonlinear estimation approach can be applied to practical systems, we focus on secure estimation for the wide area control of an interconnected power system under cyber-physical attacks and communication failures, and propose a secure estimator for the power system. Finally, we numerically show that the proposed secure estimation algorithm enables us to reconstruct the attack signals accurately. which use the synchrophasor technology to maintain the system's stability. WACS employ advanced data acquisition, communications, and control to enable increased efficiency and reliability of power delivery [12]- [14]. While WACS are the most promising technology to detect small signal instabilities in large power systems, their performance is highly dependent on the received data and on the underlying communication network. Clearly, the greater dependence on communication systems increases opportunities for cyberphysical attacks and disturbances. Extensive work has been done on monitoring and on autonomous feedback control for WACS [15], but this work has not studied how to identify cyber-physical attacks or communication failures, and how to perform secure state estimation for WACS. In this paper, we focus on secure estimation for the wide area control of an interconnected power system, and assume that the system operator has installed several phasor arXiv:1603.06894v1 [cs.SY]