Let $X$ and $Y$ be (CUN) spaces satisfying the condition (p) of S. Nakanishi.
The space $\Cal{L}(X;Y)$ consisting of all continuous linear mappings of
$X$ into $Y$ can be treated as a (UCs-N) space under the condition that:
each component space $(X_m,p_m)$ of $X$ is locally compact
and $X_{m}\subsetneqq X_{m+1}$ for each $m\in N$
and $Y_{n}\subsetneqq Y_{n+1}$ for each $n\in N$.
The main result of this paper is
to show that
a mapping of two-variables in (CUB) spaces is continuously differentiable
if and only if its partial derivatives are continuous.