One of the most active field of research in general relativity is the description of the spin properties of astrophysical objects. The main tool in the description of the gravitational waves emitted by compact binary systems in the inspiral era is the post-Newtonian (PN) approximation, where spin effects, namely, spin-orbit and spin-spin interactions, become important in higher orders. These interactions are described with coupled differential equations in general, but the PN approximation scheme gives the opportunity to solve them order by order. In the present work the effects of the spin-orbit and spin-spin interactions are described in the spin-precession equations with the use of the PN approximation up to 1.5 PN order. The decoupled angular equations describing the evolution of the direction of the spin vectors are given, and they are solved both in the eccentric and circular orbit cases. Since the spin-precession equations do not have a Newtonian contribution it is nontrivial to determine the relative order of the different variables. This analysis is also included up to the order of the spin-spin interaction.