  We introduce the so-called $d$-concavity, $d \geq 0,$ and prove that the
nonsymmetric Monge-Amp\`{e}re type function of matrix variable is concave in an
appropriate unbounded and convex set. We prove also the comparison principle
for nonsymmetric Monge-Amp\`{e}re type equations in the case when they are
so-called $\delta$-elliptic with respect to compared functions with $0 \leq
\delta <1$.
