  Motivated by the recent proof of the Stanley-Wilf conjecture, we study the
asymptotic behavior of the number of permutations avoiding a generalized
pattern. Generalized patterns allow the requirement that some pairs of letters
must be adjacent in an occurrence of the pattern in the permutation, and
consecutive patterns are a particular case of them.
  We determine the asymptotic behavior of the number of permutations avoiding a
consecutive pattern, showing that they are an exponentially small proportion of
the total number of permutations. For some other generalized patterns we give
partial results, showing that the number of permutations avoiding them grows
faster than for classical patterns but more slowly than for consecutive
patterns.
