  Let $F\subseteq\mathbb P ^{a+1}$ be a non-degenerate $K3$ surface of degree
$2a$, where $a\ge2$. In this paper we deal with Ulrich bundles on $F$ of rank
$2$. We deal with their stability and we construct $K3$ surfaces endowed with
families of non-special Ulrich bundles of rank $2$ for each $a\ge2$.
