Method for verifying the execution of a procedure of mounting/demounting a tire on/from a rim of a vehicle wheel, in the context of a process of wheel maintenance, comprising the steps of: mounting a wheel on a rotary support of a vehicle wheel maintenance apparatus, said wheel comprising a respective rim, said apparatus comprising an electric motor for putting the rotary support into rotation and at least one tool for demounting a tire from the rim or for mounting the tire on the rim; identifying a position of at least one reference point on the rim; putting the rotary support into rotation to position the wheel in a position in which the at least one reference point on the rim is located at a predetermined distance from the at least one demounting or mounting tool; and then executing the procedure of demounting the tire from the rim or mounting the tire on the rim; determining at least one position, and at least one respective value, of stress applied by the rim and/or by the demounting or mounting tool to the tire; calculating an angular distance between the position of the at least one reference point on the rim and the at least one position of stress applied by the rim and/or by the demounting or mounting tool to the tire, characterized in that it comprises the steps of: verifying that the angular distance between the position of the at least one reference point on the rim and the at least one position of stress applied by the rim and/or by the demounting or mounting tool to the tire lies within a predetermined range of acceptable distances, said range of acceptable distances being stored in memory means accessible by a control unit associated with the vehicle wheel maintenance apparatus; verifying that the at least one respective value of stress applied by the rim and/or by the demounting or mounting tool to the tire lies within a predetermined range of acceptable stress values, said range of acceptable stress values being stored in said memory means accessible by the control unit associated with the vehicle wheel maintenance apparatus, and making the results of the preceding verification steps available. mounting a wheel on a rotary support of a vehicle wheel maintenance apparatus, said wheel comprising a respective rim, said apparatus comprising an electric motor for putting the rotary support into rotation and at least one tool for demounting a tire from the rim or for mounting the tire on the rim; identifying a position of at least one reference point on the rim; putting the rotary support into rotation to position the wheel in a position in which the at least one reference point on the rim is located at a predetermined distance from the at least one demounting or mounting tool; and then executing the procedure of demounting the tire from the rim or mounting the tire on the rim; determining at least one position, and at least one respective value, of stress applied by the rim and/or by the demounting or mounting tool to the tire; calculating an angular distance between the position of the at least one reference point on the rim and the at least one position of stress applied by the rim and/or by the demounting or mounting tool to the tire, characterized in that it comprises the steps of: verifying that the angular distance between the position of the at least one reference point on the rim and the at least one position of stress applied by the rim and/or by the demounting or mounting tool to the tire lies within a predetermined range of acceptable distances, said range of acceptable distances being stored in memory means accessible by a control unit associated with the vehicle wheel maintenance apparatus; verifying that the at least one respective value of stress applied by the rim and/or by the demounting or mounting tool to the tire lies within a predetermined range of acceptable stress values, said range of acceptable stress values being stored in said memory means accessible by the control unit associated with the vehicle wheel maintenance apparatus, and making the results of the preceding verification steps available. verifying that the angular distance between the position of the at least one reference point on the rim and the at least one position of stress applied by the rim and/or by the demounting or mounting tool to the tire lies within a predetermined range of acceptable distances, said range of acceptable distances being stored in memory means accessible by a control unit associated with the vehicle wheel maintenance apparatus; verifying that the at least one respective value of stress applied by the rim and/or by the demounting or mounting tool to the tire lies within a predetermined range of acceptable stress values, said range of acceptable stress values being stored in said memory means accessible by the control unit associated with the vehicle wheel maintenance apparatus, and making the results of the preceding verification steps available.