Abstract <p> The problem of reconstructing an unknown disturbance in a nonlinear system consisting ofa combination of differential and algebraic equations is considered. Two cases are discussed. In thefirst case, the disturbance occurs in the system linearly, and in the second case, nonlinearly. In thecase of linearity, the problem has two specific features. First, it is assumed that only part of phasecoordinates of the system (namely, the coordinates described by the differential equation) isinaccurately measured at discrete times. Second, it is only known about the disturbance acting onthe system that it is an element of the space of square integrable functions; i.e., it can beunbounded. These assumptions imply the impossibility of exact reconstruction. Taking intoaccount this peculiarity, we construct a solving algorithm, which is stable with respect toinformation noises and computational errors. This algorithm is based on a combination ofelements of the theory of ill-posed problems and the extremal shift method well known in thetheory of positional differential games. A similar algorithm is designed for the general case inwhich the disturbance occurs in the system nonlinearly.</p>