  The distinctive features of equilibrium vortex structures in thin films of
anisotropic superconductors in tilted magnetic fields are studied for the
limits of moderate and strong anisotropy. The energetically favorable shape of
isolated vortex lines is found in the framework of two particular models
describing these limiting cases: London theory with an anisotropic mass tensor
and London-type model for a stack of Josephson--decoupled superconducting
layers. The increase of the field tilting is shown to result in qualitative
changes in the vortex--vortex interaction potential: the balance between
long--range attractive and repulsive forces occurs to be responsible for a
formation of a minimum of the interaction potential vs the intervortex
distance. This minimum appears to exist only for a certain restricted range of
the vortex tilting angles which shrinks with the decrease of the system
anisotropy parameter. Tilted vortices with such unusual interaction potential
form clusters with the size depending on the field tilting angle and film
thickness or/and can arrange into multiquanta flux lattice. The magnetic flux
through the unit cells of the corresponding flux line lattices equals to an
integer number $M$ of flux quanta. Thus, the increase in the field tilting
should be accompanied by the series of the phase transitions between the vortex
lattices with different $M$.
