Secondary magnesium battery having the following features: a. it comprises at least one positive electrode which contains an active material which is able to incorporate and release magnesium ions reversibly, b. it comprises at least one negative electrode which contains an active material which is able to incorporate and release magnesium ions reversibly, c. it comprises an electrolyte system composed of a solvent and a magnesium salt which is at least partially dissolved in the solvent and via which a charge exchange between the at least one positive electrode and the at least one negative electrode can take place, where the concentration of the dissolved magnesium salt in the solvent is in the range from 0.1 to 3.5 mol/l, and d. the magnesium salt has an imidazolate anion of the formula I where R 1 is - a radical from the group consisting of alkyl-, aryl-, alkylaryl-, arylalkyl-, alkyl-O-, aryl-O-, alkyl-O-alkyl-, aryl-O-aryl-, alkyl-O-aryl- and aryl-O-alkyl- where alkyl = -CH 2 -, -CH 3, -(CH 2) 2 -, -C 2 H 5, -(CH 2) 3 -, -C 3 H 7, -(CH 2) 4 -, -C 4 H 9, -(CH 2) 5 -, -C 5 H 11, -(CH 2) 6 -, -C 6 H 13 or cycloalkyl- or - an oligoether or polyether radical from the group consisting of alkyl-[O-alkyl] n -, alkyl-[O-alkyl] n -O-, aryl-[O-aryl] n -, aryl-[O-aryl] n -O-, alkyl-[O-aryl] n -, alkyl-[O-aryl] n -O-, aryl-[O-alkyl] n - and aryl-[O-alkyl] n -O- where n = 1 to 800 and alkyl = -CH 2 -, -CH 3, -(CH 2) 2 -, -C 2 H 5, - (CH 2) 3 -, -C 3 H 7, - (CH 2) 4 -, -C 4 H 9, - (CH 2) 5 -, -C 5 H 11, - (CH 2) 6 -, -C 6 H 13 or cycloalkyl- or - a substituted derivative of one of these radicals, and R 2 and R 3 are each - independently of one another electron acceptor substituents having a -I and/or -M effect which stabilise the negative charge of the imidazolate anion. a. it comprises at least one positive electrode which contains an active material which is able to incorporate and release magnesium ions reversibly, b. it comprises at least one negative electrode which contains an active material which is able to incorporate and release magnesium ions reversibly, c. it comprises an electrolyte system composed of a solvent and a magnesium salt which is at least partially dissolved in the solvent and via which a charge exchange between the at least one positive electrode and the at least one negative electrode can take place, where the concentration of the dissolved magnesium salt in the solvent is in the range from 0.1 to 3.5 mol/l, and d. the magnesium salt has an imidazolate anion of the formula I where R 1 is - a radical from the group consisting of alkyl-, aryl-, alkylaryl-, arylalkyl-, alkyl-O-, aryl-O-, alkyl-O-alkyl-, aryl-O-aryl-, alkyl-O-aryl- and aryl-O-alkyl- where alkyl = -CH 2 -, -CH 3, -(CH 2) 2 -, -C 2 H 5, -(CH 2) 3 -, -C 3 H 7, -(CH 2) 4 -, -C 4 H 9, -(CH 2) 5 -, -C 5 H 11, -(CH 2) 6 -, -C 6 H 13 or cycloalkyl- or - an oligoether or polyether radical from the group consisting of alkyl-[O-alkyl] n -, alkyl-[O-alkyl] n -O-, aryl-[O-aryl] n -, aryl-[O-aryl] n -O-, alkyl-[O-aryl] n -, alkyl-[O-aryl] n -O-, aryl-[O-alkyl] n - and aryl-[O-alkyl] n -O- where n = 1 to 800 and alkyl = -CH 2 -, -CH 3, -(CH 2) 2 -, -C 2 H 5, - (CH 2) 3 -, -C 3 H 7, - (CH 2) 4 -, -C 4 H 9, - (CH 2) 5 -, -C 5 H 11, - (CH 2) 6 -, -C 6 H 13 or cycloalkyl- or - a substituted derivative of one of these radicals, and R 2 and R 3 are each - independently of one another electron acceptor substituents having a -I and/or -M effect which stabilise the negative charge of the imidazolate anion. - a radical from the group consisting of alkyl-, aryl-, alkylaryl-, arylalkyl-, alkyl-O-, aryl-O-, alkyl-O-alkyl-, aryl-O-aryl-, alkyl-O-aryl- and aryl-O-alkyl- where alkyl = -CH 2 -, -CH 3, -(CH 2) 2 -, -C 2 H 5, -(CH 2) 3 -, -C 3 H 7, -(CH 2) 4 -, -C 4 H 9, -(CH 2) 5 -, -C 5 H 11, -(CH 2) 6 -, -C 6 H 13 or cycloalkyl- or - an oligoether or polyether radical from the group consisting of alkyl-[O-alkyl] n -, alkyl-[O-alkyl] n -O-, aryl-[O-aryl] n -, aryl-[O-aryl] n -O-, alkyl-[O-aryl] n -, alkyl-[O-aryl] n -O-, aryl-[O-alkyl] n - and aryl-[O-alkyl] n -O- where n = 1 to 800 and alkyl = -CH 2 -, -CH 3, -(CH 2) 2 -, -C 2 H 5, - (CH 2) 3 -, -C 3 H 7, - (CH 2) 4 -, -C 4 H 9, - (CH 2) 5 -, -C 5 H 11, - (CH 2) 6 -, -C 6 H 13 or cycloalkyl- or - a substituted derivative of one of these radicals, and R 2 and R 3 are each - independently of one another electron acceptor substituents having a -I and/or -M effect which stabilise the negative charge of the imidazolate anion.