In this preliminar work, an oscillatory flow contained in a closed cylinder is investigated by means of spectral methods. The problem is quite related with the Stokes boundary layer and the major phenomena belong to this region. The basic flow is axisymmetric with Z2 × O(2) symmetry that breaks into 3D when it becomes linearly unstable. For a fixed aspect ratio, Γ = 2, the locus in parameter space of the transition with the most unstable modes is obtained. Moreover, there are some indications of the location in phase space of the quasi-periodic mode that may be useful for further studies.