This paper applies ECE2 relativity to precession in the Hulse Taylor pulsar (HP) and the S2 star system. The general theory of gravitation is given for any mass m1 orbiting any mass m2. Einsteinian general relativity (EGR) is wildly incorrect by a factor of nearly forty in the HP pulsar. Using a Stanford site data, EGR gives a precession of 0.16 degrees per earth year in the HP system, and using Wikipedia data, EGR gives 0.11 degrees per earth year. The experimental result is claimed to be 4.2 degrees per earth year. EGR has been completely refuted in three hundred and seventy five papers and books of the UFT series, so these discrepancies are not surprising. In the S2 star system, EGR gives 0.203 degrees per orbit of 15.56 earth years. The experimental claims vary from – 1 degree per orbit (retrograde precession which the authors describe as violating EGR, original paper posted on this blog) and 2 degrees per orbit from another site. In S2 the weak gravitation limit holds to an excellent approximation. I cannot imagine how EGR can be claimed to be precise for the HP system. Corrections of the weak field limit to give strong gravitation are small, and cannot explain such a large discrepancy. These corrections have been severely criticised in many ways by Stephen Crothers, see “Principles of ECE”. The experimental data from different sites are also wildly self inconsistent. So we can proceed to start afresh with ECE2 relativity. As more S2 type star systems are discovered it is likely that ECE2 will succeed and EGR fail qualitatively.