On a Ru(0001) surface Cs and CO form a very well ordered (Cs+CO)-(2X2) compound layer whose structure was analyzed recently (Cs on-top, CO in threefold sites). Here we present a vibrational analysis of the same system using high-resolution electron energy loss spectroscopy (HREELS), thermal desorption spectroscopy (TDS), and low-energy electron diffraction (LEED). The bonding of CO to Ru is both local and nonlocal. Two (C-O) stretch frequencies are observed depending on whether there are one or two CO molecules in the 2X2 cell. They change in energy between 155 and 204 meV depending on CO coverage theta(CO). Setting theta(CO)(max)=1.0, the evolution of the C-O stretch intensities indicates that up to theta(CO)>0.22 the 1-CO-(2X2) phase is formed exclusively implying some mobility of the Cs layer. For theta(CO)>0.22 the 2-CO-(2x2) phase grows additionally until at theta(CO)=1.0 only the 2-CO-(2X2) phase is found. Two Ru-CO stretch modes are observed for the first time and are assigned to adsorption in the hcp and fcc hollow sites within the 2X2 unit cell. They are very weak in intensity which is attributed to the threefold-hollow site and some screening in the 2D compound. With CO adsorption a change of the electronic structure of the Cs adlayer is observed; the adlayer loses metallicity and the Cs-Ru stretch becomes visible. Strong changes of the Cs-Ru stretch energies are observed with CO coverage.