  Babson and Steingr\`imsson introduced generalized permutation patterns that
allow the requirement that two adjacent letters in a pattern must be adjacent
in the permutation. Subsequently, Claesson presented a complete solution for
the number of permutations avoiding any single pattern of type (1,2) or (2,1).
For eight of these twelve patterns the answer is given by the Bell numbers. For
the remaining four the answer is given by the Catalan numbers. In the present
paper we give a complete solution for the number of permutations avoiding a
pair of patterns of type (1,2) or (2,1). We also conjecture the number of
permutations avoiding the patterns in any set of three or more such patterns.
