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This paper suggests utilizing X-ray pulsars for relative navigation between two spacecraft in deep space. Mathematical models describing X-ray pulsar signals are presented. The pulse delay estimation problem is formulated, and the Cramér-Rao lower bound (CRLB) for estimation of the pulse delay is given. Two different pulse delay estimators are introduced, and their asymptotic performance is studied. Numerical complexity of each delay estimator, and the effect of absolute velocity errors on its performance is investigated. Using the pulsar measurements, a recursive algorithm is proposed for relative navigation between two spacecraft. The spacecraft acceleration data are provided by the inertial measurement units (IMUs). The pulse delay estimates are used as measurements, and based on models of the spacecraft and IMU dynamics, a Kalman filter is employed to obtain the 3-D relative position and velocity. Furthermore, it is shown that the relative accelerometer biases as well as the differential time between clocks can be estimated. Numerical simulations are also performed to assess the proposed navigation algorithm.