  We introduce a new class of locally compact groups, namely the strongly
compactly covered groups, which are the Hausdorff topological groups $G$ such
that every element of $G$ is contained in a compact open normal subgroup of
$G$. For continuous endomorphisms $\phi:G\to G$ of these groups we compute the
algebraic entropy and study its properties. Also an Addition Theorem is
available under suitable conditions.
