Sun-synchronous orbits (SSO) are known for the highest density of space debris population. For this reason, these orbits are often discussed in active debris removal (ADR) projects, which are to reduce pollution of the near-Earth environment. ADR missions planning is hardly possible without at least an approximate idea about the attitude dynamics of candidate objects. We have conducted a study to establish the general patterns of large debris rotational motion evolution in SSO and obtain the typical values of its parameters. Prior research indicates that attitude motion of debris objects in SSO is influenced mainly by the gravity gradient torque and the torque due to eddy currents induced by geomagnetic field. Internal energy dissipation via deformable elements and residual propellant should also be taken into account as it results in transformation of arbitrary initial motion to "flat" rotation. Qualitatively the rotational motion evolution can be divided into three stages: Transition to "flat" rotation, exponential decay and the gravitational capture. During the first relatively brief stage, the motion is primarily influenced by internal dissipation. In the second stage angular velocity decays exponentially due to eddy currents. When the object's angular velocity becomes comparable to the orbital angular velocity, the gravitational capture stage takes place exhibiting chaotic dynamics and resulting typically in the gravitational stabilization of the object. During the stage of exponential deceleration the rotation axis leans towards the orbital plane. For retrograde spins this results in capture of angular velocity vector in oscillations about the direction to the south celestial pole. This effect is the direct consequence of SSO precession. We use general formula for the torque due to eddy currents, which includes terms describing the influence of orbital motion. For fast rotations these terms are small and often neglected. However, our research shows that even for relatively large angular velocities (20-30 times greater than the orbital angular velocity) these terms can cause significant changes in the rotational axis direction for prograde spins. Furthermore, they affect final stages of rotational motion evolution and give rise to a stationary regime alternative to gravitational stabilization. In this regime the object rotates about the orbital plane normal with angular velocity equal to 1.8 of the orbital angular velocity. All stages of rotational motion evolution were studied analytically and in numerical experiments, for which we chose Ariane 4 H10 stage and defunct satellites of SPOT family.