  Nearly 10 high redshift (z>2) starburst galaxies have recently been detected
in the CO lines, revealing the early presence in the universe of objects with
large amounts of already-enriched molecular gas. The latter has sufficient
density to be excited in the high-level rotational CO lines, which yield more
flux, making easier high-redshift detections; however the effect is not as
strong as for the sub-millimeter and far-infrared dust continuum emission. With
the help of simple galaxy models, based on these first detections, we estimate
the flux in all CO lines expected for such starbursting objects at various
redshifts. We discuss the detection perspectives with the future millimeter
instruments.
