Compact binary systems that emit gravitational waves (GWs) are expected to exhibit orbital eccentricity together with generic spin configurations, leading to the precession of the orbital angular momentum, the individual spins, and the orbital plane around the total angular momentum. Although eccentric binaries with aligned spins have been extensively studied, closed-form post-Newtonian (PN) expressions that simultaneously capture both eccentricity and precessing-spin effects have remained unavailable. The presence of eccentricity significantly complicates orbital evolution, since solving the coupled differential equations generally requires numerical integration, thereby slowing waveform generation. In this work, we exploit the separation of timescales between the orbital motion, spin precession, and radiation reaction, and employ the precession-averaging method introduced by Morras et al. to effectively “average away” the explicit time dependence from the spin-orbit and spin-spin dynamics up to the second PN order. Building on this framework, we derive analytic phasing formulas from the evolution equations for the orbital frequency and eccentricity, treating eccentricity as a small parameter. Closed-form solutions for the eccentricity evolution and gravitational-wave phase are obtained up to the eighth power of the initial eccentricity $e_0$. The TaylorT2 approximant is generalized to incorporate spin-precession effects, and the orbital phase is calculated in both the time and frequency domains. To further enhance applicability, a resummation is performed on the TaylorT2 phasing formula to improve accuracy for moderate to high initial eccentricities. Taken together, these results provide efficient, closed-form phasing expressions that consistently capture the interplay of eccentricity and precessing spins, thereby enabling accurate and computationally tractable GW modeling for data analysis.

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• General relativity
• Gravitational waves