The flow between two rotating disks (radius to heigh ratio of 20.9), enclosed by a rotating cylinder, is investigated experimentally in the cases of both co- and counter-rotation. This flow gives rise to a large gallery of instability patterns. A regime diagram of these patterns is presented in the (Reb,Ret)-plane, where Reb,t is the Reynolds number associated with each disk. The co-rotation case and the weak counter-rotation case are very similar to the rotor–stator case, both for the basic flow and the instability patterns: the basic flow consists of two boundary layers near each disk and the instability patterns are the axisymmetric vortices and the positive spirals described in the rotor–stator experiments of Gauthier, Gondret & Rabaud (1999), Schouveiler, Le Gal & Chauve (2001), and the numerical study of Serre, Crespo del Arco & Bontoux (2001). The counter-rotation case with higher rotation ratio is more complex: above a given rotation ratio, the recirculation flow becomes organized into a two-cell structure with the appearance of a stagnation circle on the slower disk. A new kind of instability pattern is observed, called negative spirals. Measurements of the main characteristics of this pattern are presented, including growth times, critical modes and phase velocities.