We show that the product of a compact sequential Hausdorff space, with an absolutely countably compact regular space is absolutely countably compact, and we give several related results. For example, we show that every countably compact generalized ordered space is absolutely countably compact, and that the product of a compact Hausdorff space of countable tightness with an absolutely countably compact, $\omega$-bounded regular space (in particular a countably compact generalized ordered space) is absolutely countably compact. The main results answer questions of M. Matveev.