The Galilean and 'dual' invariant electrodynamics with magnetic charges is formulated. The definition of the main feature of relativistic electromagnetism is given. Consideration of different aspects of Galilean electromagnetism with magnetic charges is presented. It is shown in particular that the conclusion of Bacry & Kubar-Andre (1973) that the existence of the magnetic monopole is incompatible with Galilean invariance in general appears to be incorrect. There jq (jg) is the density of electric (magnetic) current, pq (pg) is the density of electric (magnetic) charge, (cp, j) is a current four-vector, jq = £iJqi, Jg = £iJgi, Oq = ~iPqi, Pg = £i Pgi and subscript (i) indicates a dual charged particles with charges qi and gi, and eo/a o (two constants) are defined in the usual way.Postal address: Dr. V. I. Strazhev,