  A perfect matching in the complete graph on $2k$ vertices is a set of edges
such that no two edges have a vertex in common and every vertex is covered
exactly once. Two perfect matchings are said to be $t$-intersecting if they
have at least $t$ edges in common. The main result in this paper is an
extension of the famous Erd\H{o}s-Ko-Rado (EKR) theorem \cite{EKR} to
2-intersecting families of perfect matchings for all values of $k$.
Specifically, for $k\geq 3$ a set of 2-intersecting perfect matchings in
$K_{2k}$ of maximum size has $(2k-5)(2k-7)\cdots (1)$ perfect matchings.
