  Two structures are said to be equimorphic if each embeds in the other. Such
structures cannot be expected to be isomorphic, and in this paper we
investigate the special case of linear orders, here also called chains. In
particular we provide structure results for chains having less than continuum
any isomorphism classes of equimorphic chains. We deduce as a corollary that
any chain has either a single isomorphism class of equimorphic chains or
infinitely many.
