A servo-hydraulic drive for position control with a flapper-nozzle type servo-valve is described by a 10th-order, non-linear system of ODEs. This system is partially singularly perturbed. The perturbation stems from the compressibility of the hydraulic fluid and the fast dynamics of some sub-systems of the valve. Center manifold theory in the version due to Fenichel is used to study the behavior of the drive system in the case of periodic motions. The insufficient differentiability properties of the system prevent the direct application of Fenichel's theorems. Thus, phase space is decomposed into sub-spaces each with sufficient differentiability properties. There, limit sets of the system can be given as the solution of the reduced problem. Approximate analytical solutions are derived for that. At the boundaries of adjacent sub-spaces transition layers occur which connect these limit set trajectories of adjacent sub-spaces. The order of magnitude of these transition layers is estimated by asymptotic expansions. Further, a comment is given on the stability properties. Stability is strongly affected by the small perturbation parameters and is most critical in the resting position of the drive. Theoretical results are compared with numerical computations and experiments.