  Let $K$ be a field and $X$ a connected partially ordered set. In the first
part of this paper, we show that the finitary incidence algebra $FI(X,K)$ of
$X$ over $K$ has an involution of the second kind if and only if $X$ has an
involution and $K$ has an automorphism of order $2$. We also give a
characterization of the involutions of the second kind on $FI(X,K)$. In the
second part, we give necessary and sufficient conditions for two involutions of
the second kind on $FI(X,K)$ to be equivalent in the case where $char K\neq 2$
and every multiplicative automorphism of $FI(X,K)$ is inner.
