  We study genus 1 Gromov-Witten invariants of Fano complete intersections in
the projective spaces. Among other things, we show a reconstruction theorem for
genus 1 invariants with only ambient insertions, and compute the genus 1
invariants with 1 marked point. For cubic hypersurfaces of dimension $\neq 4$
and odd dimensional intersections of two quadrics, we obtain a complete
reconstruction theorem for genus 1 Gromov-Witten invariants.
