  We study growth of absolute and homological $k$-dimensional systoles of
arithmetic $n$-manifolds along congruence coverings. Our main interest is in
the growth of systoles of manifolds whose real rank $r > 1$. We observe, in
particular, that in some cases for $k = r$ the growth function tends to
oscillate between a power of a logarithm and a power function of the degree of
the covering. This is a new phenomenon. We also prove the expected
polylogarithmic and constant power bounds for small and large $k$,
respectively.
