The application of differential algebra (DA) and Taylor models to the analysis and prediction of near Earth objects close encounters is investigated. The high order expansion of the flow of ordinary differential equations obtained by DA is exploited to develop tools for the prediction of planetary encounters and potential impacts, which takes into account the uncertainties due to measurement accuracy. Furthermore, Taylor model integrators are employed for the long-term rigorous integration of the motion of near Earth objects, considering the set of possible initial conditions expressed as interval boxes. A variety of dynamical models and ephemeris functions are developed, tailored to the evaluation in the differential algebra and Taylor model frames. Apophis close encounter in 2029 and the resonant return in 2036 are used as test cases.