  The existence and exact form of the continuum expression of the discrete
nonlogarithmic $q$-entropy is an important open problem in generalized
thermostatistics, since its possible lack implies that nonlogarithmic
$q$-entropy is irrelevant for the continuous classical systems. In this work,
we show how the discrete nonlogarithmic $q$-entropy in fact converges in the
continuous limit and the negative of the $q$-entropy with continuous variables
is demonstrated to lead to the (Csisz{\'a}r type) $q$-relative entropy just as
the relation between the continuous Boltzmann-Gibbs expression and the
Kullback-Leibler relative entropy. As a result, we conclude that there is no
obstacle for the applicability of the $q$-entropy to the continuous classical
physical systems.
