We generalise Uspensky's theorem characterising eventual exact (e.e.) covers
of the positive integers by homogeneous Beatty sequences, to e.e. m-covers, for
any m \in \N, by homogeneous sequences with irrational moduli. We also consider
inhomogeneous sequences, again with irrational moduli, and obtain a purely
arithmetical characterisation of e.e. m-covers. This generalises a result of
Graham for m = 1, but when m > 1 the arithmetical description is more
complicated. Finally we speculate on how one might make sense of the notion of
an exact m-cover when m is not an integer, and present a "fractional version"
of Beatty's theorem.