In this paper, the problem of partial attitude synchronization between spacecraft with fewer than three control torques is formulated and solved for the first time. Considering a network of N underactuated spacecraft, we propose two control strategies to align the uncontrolled axes of the spacecraft such that they all point along the same inertial direction. The first control law achieves this objective using inertial angular velocity feedback and, as a result, the final, common, pointing direction of the uncontrolled axes of all spacecraft remains fixed in inertial space. The final direction may also be prescribed with the presence of a leader. The second control law achieves the same objective by relying upon only relative angular velocity feedback. In this case the final pointing direction of the uncontrolled axes is no longer fixed in the inertial space. The control laws utilize a unique attitude parameterization capable of decoupling the motion between the uncontrolled axis of each spacecraft and the spacecraft's angular orientation about this axis. Subject to the proposed control laws, it is shown that the spacecraft network's partial consensus state is almost globally asymptotically stable. (C) 2018 Elsevier Ltd. All rights reserved.