In an engine having apparatus for a post-exhaust process, surging is prevented when the air excess coefficient is changed to a lean condition from a rich condition in order to carry out the post-exhaust process. The present engine control apparatus comprises a turbo-supercharger driven by exhaust energy of an engine in a vehicle, an EGR path interconnecting an exhaust path and an inlet path of the engine, at least one of a NO.sub.x trap catalyzer and a diesel particulate filter (DPF) mounted in the exhaust path for purifying exhaust discharged from the engine, an EGR valve for adjusting the flow rate of air passing through the EGR path, an air excess coefficient control unit for controlling the air excess coefficient, depending on driving conditions, and wherein the EGR valve is operable to close when the air coefficient control unit controls the air excess coefficient so as to be in a lean condition.