Using an index theory for countably condensing maps, we show the existence of eigenvalues for countably k-set contractive maps and countably condensing maps in an infinite dimensional Banach space X, under certain condition that depends on the quantitative haracteristic, that is, the infimum of all $k;{geq};1$ for which there is a countably k-set-contractive retraction of the closed unit ball of X onto its boundary.