  We give a theoretical description of the general critical states in which the
critical currents in type-II superconductors are not perpendicular to the local
magnetic induction. Such states frequently occur in real situations, e.g., when
the sample shape is not sufficiently symmetric or the direction of the external
magnetic field changes in some complex way. Our study is restricted to the
states in which flux-line cutting does not occur. The properties of such
general critical states can essentially differ from the well-known properties
of the usual Bean critical states. To illustrate our approach, we analyze
several examples. In particular, we consider the critical states in a slab
placed in a uniform perpendicular magnetic field and to which two components of
the in-plane magnetic field are then applied successively. We also analyze the
critical states in a long thin strip placed in a perpendicular magnetic field
which then is tilted towards the axis of the strip.
