Several recent papers describe closed loop fuel-air ratio control systems designed to operate at stoichiometric conditions because of the high three-way catalyst conversion efficiencies which occur only in a narrow band around stoichiometric. This paper investigates closed loop control of fuel-air ratio using a temperature compensated zirconia sensor at other than stoichiometric conditions. If engines can be made to run at very lean(Φ≈0.6-0.7) equivalence ratios through greater attention to proper fuel-air mixing and vaporization, CO, HC, and NOx emissions are minimized simultaneously. Closed loop control in the lean region makes the system insensitive to parameter variations and allows the fuel-air ratio to be maintained closer to the lean limit than would be possible under conventional open loop conditions.Assuming lean combustion and using the Nernst equation for the oxygen sensor, equations are derived relating equivalence ratio to the oxygen sensor output voltage and temperature. Equations are also derived and discussed which give the sensitivity of predicted equivalence ratio to measurement errors in voltage and temperature and to variations in humidity and exhaust pressure. A simplified calculation scheme, which involves a linearization in equivalence ratio and which might be used in an onboard computer, is presented and its accuracy is discussed.The theoretical results are verified using experimental data obtained on a CFR engine and a system is described which predicts and controls fuel-air ratio closed loop in the lean region based on oxygen sensor and thermocouple output voltages.