  We consider a two-parameter family of R\'enyi relative entropies
$D_{\alpha,z}(\rho||\sigma)$ that are quantum generalisations of the classical
R\'enyi divergence $D_{\alpha}(p||q)$. This family includes many known relative
entropies (or divergences) such as the quantum relative entropy, the recently
defined quantum R\'enyi divergences, as well as the quantum R\'enyi relative
entropies. All its members satisfy the quantum generalizations of R\'enyi's
axioms for a divergence. We consider the range of the parameters $\alpha,z$ for
which the data processing inequality holds. We also investigate a variety of
limiting cases for the two parameters, obtaining explicit formulas for each one
of them.
