I. INTRODUCTION The papers [1], [2] by Dirac, in which the existence of magnetic charges was related to quantization of electrical charges, were followed by intensively searching for magnetic monopoles, however, the search has not yet led to success (see, for example, [3]). All the attempts of such search were complicated by the lack of a satisfactory theoretical descrip- tion of interactions between ordinary electrical and magnetic charges. Moreover, Rohrlich in [4] stated the ”falsehood of variational principle for the full theory of . . . electrical and magnetic point charges”. Later, Zwanziger in [5] proposed the full action including an ar- bitrary constant 4-vector n , with the electromagnetic field propagator being dependent of the arbitrary vector n ; as a result, for a partial case of interaction between an electrical charge and a magnetic charge, when the dependence is not reduced, we come to an absurd result - the cross-section of interaction of the electrical and magnetic charges depends on the arbitrary constant vector. If everything were valid in Zwanziger’s considerations, impos- sibility of the existence of magnetic charges would follow (or implication that something is wrong in relativistic quantum field theory). Hence, the full action construction for a system of interacting electrical and magnetic charges (and clarification of the cause of “failure” in efforts by Zwanziger) is the matter of principle. The paper proposes the full action for an electromagnetic field with electrical and mag- netic charges and mentions, in passing, that the expression for the Lagrangian of interaction between electrical and magnetic charges and an external field, used in the paper by Zwanziger [5] without discussions, is not correct. We do not consider particles with both electrical and magnetic charges (compare with the statement by Weinberg in [6] that “a magnetic monopole cannot bear a normal charge”). The expressions below are written in Gaussian units. The denotations we use are close to that used in [7] and [8], in particular, the coordinate indexes of vectors and tensors have values from 0 to 3; a metrics is considered to be defined with diagonal metric tensor g : g ik = 0 at i = k , g 00 = 1, g 11 = g 22 = g 33 = − 1; the same upper and lower coordinate indexes of four-dimensional tensors always imply summation; if some indexes are not coordinate tensor indexes, the summation symbol is explicitly shown, if necessary; the four-dimensional coordinate is x i = ( ct, r ), x$_{i}$ = ( ct, − r ), x $^{i}$x$_{i}$ = c $^{2}$t2 − r $^{2}$, where c is the light speed constant, t is time, r is three-dimensional radius-vector. 2