  Copula models have become popular in different applications, including
modeling shocks, in view of their ability to describe better the dependence
concepts in stochastic systems. The class of maxmin copulas was recently
introduced by Omladi\v{c} and Ru\v{z}i\'{c}. It extends the well known classes
of Marshall-Olkin and Marshall copulas by allowing the external shocks to have
different effects on the two components of the system. By a reflection (flip)
in one of the variables we introduce a new class of bivariate copulas called
reflected maxmin (RMM) copulas. We explore their properties and show that
symmetric RMM copulas relate to general RMM copulas similarly as do semilinear
copulas relate to Marshall copulas. We transfer that relation also to maxmin
copulas. We also characterize possible diagonal functions of symmetric RMM
copulas.
