  In this paper, we study triple derivations and triple homomorphisms of
perfect Lie superalgebras over a commutative ring $R$. It is proved that, if
the base ring contains $\frac{1}{2}$, $L$ is a perfect Lie superalgebra with
zero center, then every triple derivation of $L$ is a derivation, and every
triple derivation of the derivation algebra $ Der (L)$ is an inner derivation.
Let $L,~L^{'}$ be Lie superalgebras over a commutative ring $R$, the notion of
triple homomorphism from $L$ to $L^{'}$ is introduced. We proved that, under
certain assumptions, homomorphisms, anti-homomorphisms, and sums of
homomorphisms and anti-homomorphisms are all triple homomorphisms.
