In this paper we present high resolution spectroscopy performed with femtosecond coherent anti-Stokes Raman scattering (CARS). After a theoretical treatment of the issue, specific experimental configurations will be introduced. Transients from nonresonant rotational and vibrational CARS on di- and polyatomics in the gas phase were analyzed. Rotational and vibrational constants and pressure-dependent line shifts are determined with high accuracy. The method is suitable for precise measurement of temperatures. We present thermometry on combustion relevant species like H-2 and N-2 and discuss the reliability and accuracy of the data.