  We construct secondary cup and cap products on coarse (co-)homology theories
from given cross and slant products. They are defined for coarse spaces
relative to weak generalized controlled deformation retracts.
  On ordinary coarse cohomology, our secondary cup product agrees with a
secondary product defined by Roe. For coarsifications of topological coarse
(co-)homology theories, our secondary cup and cap products correspond to the
primary cup and cap products on Higson dominated coronas via transgression
maps. And in the case of coarse $\mathrm{K}$-theory and -homology, the
secondary products correspond to canonical primary products between the
$\mathrm{K}$-theories of the stable Higson corona and the Roe algebra under
assembly and co-assembly.
