We discuss the cosmological degeneracy of the age of the Universe, the Hubble parameter and the effective number of relativistic particles Neff. We show that independent determinations of the Hubble parameter H(z) such as those recently provided by Simon et al (2005 Phys. Rev. D 71 123001), combined with other cosmological data sets, can provide the most stringent constraints on Neff, yielding Neff = 3.7-1.2+1.1 at 95% confidence level. A neutrino background is detected with high significance: Neff>1.8 at better than 99% confidence level. Constraints on the age of the Universe in the framework of an extra background of relativistic particles are improved by a factor of 3.