For a discrete group \(\Gamma\) and an integer \(n\), finiteness properties \(FP_n\) and \(F_n\) are considered. They are defined as follows: \(\Gamma\) is of type \(FP_n\) if there is a projective resolution of \(\mathbb{Z} \Gamma\) over the trivial \(\mathbb{Z} \Gamma\)-module \(\mathbb{Z}\) with finitely generated modules in dimension \(\leq n\). \(\Gamma\) is of type \(F_n\) if there is an Eilenberg-MacLane space \(K (\Gamma,1)\) with finite \(n\)-skeleton. In the paper under review, the authors introduce, as a generalization, compactness properties \(CP_n\) and \(C_n\) for a locally compact group \(G\). They show that, as in the discrete case, \(C_1\) is equivalent to compact generation and \(C_2\) is equivalent to compact presentability. Moreover, it is proved that the compactness properties are preserved by some operations as passing to a cocompact subgroup or to the quotient by a compact normal subgroup.