  We study locally Cohen-Macaulay curves in projective three-space which are
contained in a double plane 2H, thus completing the classification of curves
lying on surfaces of degree two. We describe the irreducible components of the
Hilbert schemes of locally Cohen-Macaulay curves in 2H of given degree and
arithmetic genus. We show that these Hilbert schemes are connected. We also
discuss the Rao modules of these curves, and liaison and biliaison equivalence
classes.
