The post-deposition dc electrical-resistance increase of island copper films deposited on glass substrates at room temperature and at a pressure of 2×10-5 torr is studied. Films in the resistance range 10-95 M/ were studied under different conditions to ascertain the role of residual gases and substrate-surface contaminants on the agglomeration rate. Mobility coalescence of small islands of Cu giving rise to an agglomerated film structure is assumed to explain the post-deposition resistance increase. It was found that the logarithm of the normalized resistance [ln(R/R0); R0 is the initial resistance of the film at a time t=0] varies linearly as the logarithm of the time elapsed after the cessation of deposition. The constant of proportionality in the above relationship, termed the agglomeration rate m, shows an interesting oscillatory dependence on the initial resistance of the film and the condition of study. Nearly all the maxima and minima of m for two of the conditions studied in detail as a function of the initial resistance occur at about the same initial resistance values with the films having almost the same structure at these points. An argument is put forward based on the oscillatory nature of the effective tunneling barrier as a function of the island size to explain this unusual behavior. It is found that the presence of a thin film of water vapor on the substrate surface impedes the agglomeration rate to a great extent while the presence of adsorbed O2 and N2 decreases the energy for surface migration of islands of copper thereby increasing the agglomeration rate.