  We study genus 2 covers of relative elliptic curves over an arbitrary base in
which 2 is invertible. Particular emphasis lies on the case that the covering
degree is 2. We show that the data in the "basic construction" of genus 2
covers of relative elliptic curves determine the cover in a unique way (up to
isomorphism).
  A classical theorem says that a genus 2 cover of an elliptic curve of degree
2 over a field of characteristic different from 2 is birational to a product of
two elliptic curves over the projective line. We formulate and prove a
generalization of this theorem for the relative situation.
  We also prove a Torelli theorem for genus 2 curves over an arbitrary base.
