Abstract: The dissertation presents non-equilibrium chemical kinetic studies of large volume lean gaseous hydrocarbon/ air mixture combustion at temperatures (~300K) much below self ignition temperatures and low pressures (40-80torr), in ~25 nanosecond duration repetitive high voltage (~18kV) electric discharges running at 10 Hz. Xenon calibrated Two Photon Absorption Laser Induced Fluorescence (TALIF) is used to measure absolute atomic oxygen concentrations in air, methane-air, and ethylene-air non-equilibrium plasmas, as a function of time after initiation of a single 25 nsec discharge pulse at 10Hz. Oxygen atom densities are also measured after a burst of nanosecond discharges at a variety of delay times, the burst being run at 10Hz. Each burst contains sequences of 2 to 100 nanosecond discharge pulses at 100 kHz. Burst mode measurements show very significant (up to ~0.2%) build-up of atomic oxygen density in air, and some build-up (by a factor of approximately three) in methane-air at [phi]=0.5. Burst measurements in ethylene-air at [phi]=0.5 show essentially no build-up, due to rapid O atom reactions with ethylene in the time interval between the pulses. Nitric oxide density is also measured using single photon Laser Induced Fluorescence (LIF), in a manner similar to oxygen atoms, and compared with kinetic modeling. Fluorescence from a NO (4.18ppm) +N2 calibration gas is used to calibrate the NO densities. Peak density in air is found to be ~ 3.5ppm at ~ 225us, increasing from almost initial levels of ~ 0 ppm directly after the pulse. Kinetic modeling using only the Zeldovich mechanism predicts a slow increase in NO formation, in ~ 2 ms, which points towards the active participation of excited N2 and O2 molecules and N atoms in forming NO molecules. Ignition delay at a variety of fuel/ air conditions is studied using OH emission measurements at ~ 308nm as ignition foot prints. The ignition delay is found to be in the range of 6-20ms for ethylene/ air mixtures. No ignition was observed in the case of methane/ air mixtures. All these measurements agree well with kinetic modeling developed involving plasma reactions and electron energy distribution function calculations.