  Let $\mathcal{C}_n$ denote the set of words $w=w_1\cdots w_n$ on the alphabet
of positive integers satisfying $w_{i+1}\leq w_i+1$ for $1 \leq i \leq n-1$
with $w_1=1$. The members of $\mathcal{C}_n$ are known as Catalan words and are
enumerated by the $n$-th Catalan number $C_n$. The problem of finding the
cardinality of various avoidance classes of $\mathcal{C}_n$ has been an ongoing
object of study, and members of $\mathcal{C}_n$ avoiding one or two classical
or a single consecutive pattern have been enumerated. In this paper, we extend
these results to vincular patterns and seek to determine the cardinality of
each avoidance class corresponding to a pattern of type (1,2) or (2,1). In
several instances, a simple explicit formula for this cardinality may be given.
In the more difficult cases, we find only a formula for the (ordinary)
generating function which enumerates the class in question. We make extensive
use of functional equations in establishing our generating function results.
