  We establish the theorems that give necessary and sufficient conditions for
an arbitrary function defined in the unit disk of complex plane in order to has
boundary values along classes of equivalencies of simple curves. Our results
generalize the well--known theorems on asymptotic and angular boundary behavior
of meromorphic functions (Lindolf, Lehto--Virtanen, and Seidel--Walsh type
theorems). The results are applied to the study of boundary behavior of
meromorphic functions along curves using $P-$sequences, as well as in the proof
of the uniqueness theorem similar to Saginjan's one.
  Constructed examples of functions show that the results cannot be improved.
