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Motivated by the complexity and the large quantity of on-line operations required for nonlinear filtering problems, observers for nonlinear stochastic systems are constructed based on a Lyapunov-like method. Sufficient conditions on the structure of a nonlinear stochastic system for the existence of an exponentially bounded observer are given. These conditions can be applied off-line. The stabilization of unstable nonlinear stochastic systems using observer feedback are investigated. Sufficient conditions to stabilize cascaded control and observer in a feedback arrangement are given.