The invention discloses a process and a production system for synthesizing dimethyl oxalate or diethyl oxalate and coproducing oxalic acid. The method comprises the following steps of: reacting nitrogen oxide with alcohol in an esterification reactor to form nitrite, adding the nitrite into a gas phase coupling carbonylation reactor, and connecting the gas phase coupling carbonylation reactor with a condenser and an oxalate hydrolysis reactor. After being condensed by the condenser, outlet gas of the gas phase coupling carbonylation reactor is condensed into liquid-phase or solid-phase oxalate; the oxalate in the gas phase enters the oxalate hydrolysis reactor to generate the oxalic acid and the alcohol of corresponding ester; the ester solution of the corresponding ester can enter the subsequent esterification reactor for reaction; and the amount of the oxalate which enters the gas phase can be adjusted by adjusting the temperature of the condenser so as to adjust the distribution of the synthetic amount of the oxalate and the oxalic acid. Nitrogen oxide-containing noncondensable gas which passes through the oxalate hydrolysis reactor is recycled to enter the esterification reactor so as to realize the recycling of the nitrogen oxide. The process and the production system for synthesizing the dimethyl oxalate or the diethyl oxalate and coproducing the oxalic acid have low energy consumption and high productivity and meet the industrial requirement.