  Over the $(1,n)$-dimensional real supercircle, we consider the
$\mathcal{K}(n)$-modules of linear differential operators,
$\frak{D}^n_{\lambda,\mu}$, acting on the superspaces of weighted densities,
where $\mathcal{K}(n)$ is the Lie superalgebra of contact vector fields. We
give, in contrast to the classical setting, a classification of these modules
for $n=1$. We also prove that $\frak{D}^{n}_{\lambda,\mu}$ and
$\frak{D}_{\rho,\nu}^{n}$ are isomorphic for $\rho=\frac{2-n}{2}-\mu$ and
$\nu=\frac{2-n}{2}-\lambda$. This work is the simplest superization of a result
by Gargoubi and Ovsienko [Modules of Differential Operators on the Real Line,
Functional Analysis and Its Applications, Vol. 35, No. 1, pp. 13--18, 2001.]
