A model of the time-dependent chemistry of dense interstellar clouds is formulated to study the dominant chemical processes in carbon and oxygen isotope fractionation, the formation of nitrogen-containing molecules, and the evolution of product molecules as a function of cloud density and temperature. The abundances of the dominant isotopes of the carbon- and oxygen-bearing molecules are calculated. The chemical abundances are found to be quite sensitive to electron concentration since the electron concentration determines the ratio of H3(+) to He(+), and the electron density is strongly influenced by the metals abundance. For typical metal abundances and for H2 cloud density not less than 10,000 molecules/cu cm, nearly all carbon exists as CO at late cloud ages. At high cloud density, many aspects of the chemistry are strongly time dependent. Finally, model calculations agree well with abundances deduced from observations of molecular line emission in cold dense clouds.