  We extend an axiomatic approach to classical electrodynamics, which we
developed recently, to the case of non-vanishing magnetic charge. Then two
axioms, namely those of the existence of the Lorentz force (Axiom 2) and of
magnetic flux conservation (Axiom 3) have to be generalized. Electric/magnetic
reciprocity constitutes a guiding principle for this undertaking. The extension
of the axioms can be implemented at a premetric stage, i.e., when metric and
connection of spacetime don't play a role. Complex Riemann-Silberstein fields
of the form $(E\pm i {\cal H},{\cal D}\pm i B)$ have a natural place in the
theory, independent of the Hodge duality mapping defined by any particular
metric.
