The influence of the small neutrino mass on the properties of the cosmological neutrino gas and on the evolution of the universe is estimated. The characteristics of the equilibrium neutrino gas are first calculated and the temperatures up to which to which they can be regarded as ultrarelativistic for different neutrino masses are found. The evolution of cosmological neutrinos of any type are traced for different neutrino masses. The red shifts neutrinos remain ultrarelativistic are determined. The effective temperature of the neutrino gas and the effect of neutrino mass on the rate of expansion of the universe are determined.