Process for preparing methacrylic acid and/or methacrylic esters, comprising the process steps (a) conversion of isobutene, tert-butanol or a mixture containing isobutene and/or tert-butanol in a first catalytic gas-phase oxidation step to give a reaction product mainly containing methacrolein, (b) conversion of the reaction product mainly containing methacrolein from process step (a) in a second catalytic gas-phase oxidation step to give a gaseous reaction product consisting predominantly of methacrylic acid and unconverted methacrolein, (c) removal, preliminary purification and condensation of a portion of the unconverted methacrolein accumulating in the gaseous reaction product in process step (b) to form a liquid recycle methacrolein fraction, (d) transfer of the recycle methacrolein fraction into a gaseous stream and (e) conversion of this gaseous recycle methacrolein stream in a catalytic oxidation step, characterized in that process step (d) comprises the process aspects of i) uniform distribution of the liquid recycle methacrolein fraction obtained in step c) in the form of droplets on the surface of a packing to obtain a liquid film, ii) contacting of the liquid film obtained in step (i) with a gas stream containing 3% to 21% by volume of oxygen and having a temperature which is 10 to 150°C higher than the temperature of the liquid methacrolein, to obtain a gas mixture containing recycle methacrolein, iii) optional mixing of the gas stream obtained according to (ii) with additional steam and iv) mixing of the resulting gas stream, containing methacrolein, oxygen, steam, nitrogen and other organic compounds having 1 to 6 carbon atoms, with the reaction product of the first oxidation stage (a). (a) conversion of isobutene, tert-butanol or a mixture containing isobutene and/or tert-butanol in a first catalytic gas-phase oxidation step to give a reaction product mainly containing methacrolein, (b) conversion of the reaction product mainly containing methacrolein from process step (a) in a second catalytic gas-phase oxidation step to give a gaseous reaction product consisting predominantly of methacrylic acid and unconverted methacrolein, (c) removal, preliminary purification and condensation of a portion of the unconverted methacrolein accumulating in the gaseous reaction product in process step (b) to form a liquid recycle methacrolein fraction, (d) transfer of the recycle methacrolein fraction into a gaseous stream and (e) conversion of this gaseous recycle methacrolein stream in a catalytic oxidation step, i) uniform distribution of the liquid recycle methacrolein fraction obtained in step c) in the form of droplets on the surface of a packing to obtain a liquid film, ii) contacting of the liquid film obtained in step (i) with a gas stream containing 3% to 21% by volume of oxygen and having a temperature which is 10 to 150°C higher than the temperature of the liquid methacrolein, to obtain a gas mixture containing recycle methacrolein, iii) optional mixing of the gas stream obtained according to (ii) with additional steam and iv) mixing of the resulting gas stream, containing methacrolein, oxygen, steam, nitrogen and other organic compounds having 1 to 6 carbon atoms, with the reaction product of the first oxidation stage (a).