  For $i=2,3$ and a cubic graph $G$ let $\nu_{i}(G)$ denote the maximum number
of edges that can be covered by $i$ matchings. We show that $\nu_{2}(G)\geq
{4/5}| V(G)| $ and $\nu_{3}(G)\geq {7/6}| V(G)| $. Moreover, it turns out that
$\nu_{2}(G)\leq \frac{|V(G)|+2\nu_{3}(G)}{4}$.
