  We study interaction-induced broken symmetry phases that can arise in
metallic or semimetallic band structures with two nested Weyl or Dirac loops.
The odered phases can be of the charge or (pseudo)spin density wave type, or
superconductivity from interloop pairing. A general analysis for two types of
Weyl loops is given, according to whether a local reflection symmetry in
momentum space exists or not, for Hamiltonians having a global PT symmetry. The
resulting density-wave phases always have lower total energy, and can be
metallic, insulating, or semimetallic (with nodal loops), depending on both the
reflection symmetry of the loops and the symmetry transformation that maps one
loop onto the other. We extend this study to nested $\mathbb{Z}_2$ nodal lines,
for which the ordered phases include also nodal point and nodal chain
semimetals, and to spinful Dirac nodal lines. Superconductivity from interloop
pairing can be fully gapped only if the initial double loop system is
semimetallic.
