  Varying the angle Theta between applied field and the conducting planes of a
layered superconductor in a small interval close to the plane-parallel field
direction, a large number of superconducting states with unusual properties may
be produced. For these states, the pair breaking effect of the magnetic field
affects both the orbital and the spin degree of freedom. This leads to pair
wave functions with finite momentum, which are labeled by Landau quantum
numbers 0<n<\infty. The stable order parameter structure and magnetic field
distribution for these states is found by minimizing the quasiclassical free
energy near H_{c2} including nonlinear terms. One finds states with coexisting
line-like and point-like order parameter zeros and states with coexisting
vortices and antivortices. The magnetic response may be diamagnetic or
paramagnetic depending on the position within the unit cell. The structure of
the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states at Theta=0 is reconsidered.
The transition n->\infty of the paramagnetic vortex states to the FFLO-limit is
analyzed and the physical reason for the occupation of higher Landau levels is
pointed out.
