  This note describes minimal surfaces $S$ of general type satisfying $p_g\geq
5$ and $K^2=2p_g$. For $p_g\geq 8$ the canonical map of such surfaces is
generically finite of degree 2 and the bulk of the paper is a complete
characterization of such surfaces with non birational canonical map. It turns
out that if $p_g\geq 13$, $S$ has always an (unique) genus 2 fibration, whose
non 2-connected fibres can be characterized, whilst for $p_g\leq 12$ there are
two other classes of such surfaces with non birational canonical map.
