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We present a sky simulation of the atomic HI-emission line and the first 10 rotational CO emission lines of molecular gas in galaxies beyond the Milky Way. The simulated sky field has a comoving diameter of 500 Mpc/h; hence, the actual field-of-view depends on the (user-defined) maximal redshift zmax; e. g., for zmax=10, the field of view yields 4x4 deg^2. For all galaxies, we estimate the line fluxes, line profiles, and angular sizes of the Hi and CO-emission lines. The galaxy sample is complete for galaxies with cold hydrogen masses above 10^8 Msun. This sky simulation builds on a semi-analytic model of the cosmic evolution of galaxies in a Lambda-cold dark matter (Lambda CDM) cosmology. The evolving CDM distribution was adopted from the Millennium Simulation, an N-body CDM-simulation in a cubic box with a side length of 500 Mpc/h. This side length limits the coherence scale of our sky simulation: it is long enough to allow the extraction of the baryon acoustic oscillations in the galaxy power spectrum, yet the position and amplitude of the first acoustic peak will be imperfectly defined. This sky simulation is a tangible aid to the design and operation of future telescopes, such as the Square Kilometre Array, Large Millimeter Telescope, and Atacama Large Millimeter/submillimeter Array. The results presented in this paper have been restricted to a graphical representation of the simulated sky and fundamental dN/dz-analyses for peak flux density limited and total flux limited surveys of Hi and CO. A key prediction is that HI will be harder to detect at redshifts z>2 than predicted by a no-evolution model. The future verification or falsification of this prediction will allow us to qualify the semi-analytic models.