  Both the Kullback-Leibler and the Tsallis divergence have a strong
limitation: if the value $0$ appears in probability distributions $\left(
p_{1},\cdots ,p_{n}\right)$ and $\left( q_{1},\cdots ,q_{n}\right)$, it must
appear in the same positions for the sake of significance. In order to avoid
that limitation in the framework of Shannon statistics, Ferreri introduced in
1980 the hypoentropy: "such conditions rarely occur in practice". The aim of
the present paper is to extend Ferreri's hypoentropy to the Tsallis statistics.
We introduce the Tsallis hypoentropy and the Tsallis hypodivergence and
describe their mathematical behavior. Fundamental properties like
nonnegativity, monotonicity, the chain rule and subadditivity are established.
