  We investigate vortex structure and melting transition in very anisotropic
layered superconductors at fields tilted with respect to the c-axis. We show
that even a small in-plane field does not homogeneously tilt the vortex lattice
but, instead, penetrates inside the superconductor in the form of Josephson
vortices (JVs) similar to the Meissner state. At high c-axis magnetic field the
phase field of the JV is built up from the phase perturbations created by
displacements of pancake vortices. The crossing-lattices ground state leads to
linear dependencies of the melting field and melting temperature on the
in-plane field, in agreement with recent experimental observations. At small
fields stacks of JVs accumulate additional pancake strings creating vortex rows
with enhanced density. This mechanism explains the mixed chains-lattice state
observed by Bitter decorations.
