The invention relates to a wire implant, in particular for wire osteosynthesis, and a corresponding method for its production. The wire implant has been subjected to a heat treatment, wherein the wire implant consists of a biocompatible, biocorrodible magnesium alloy, which is composed of metallic magnesium of at least 80 wt. % a zinc proportion of 0.1 to 2.0 wt. %, a zirconium proportion of 0.1 to 2.0 wt. %, a proportion of rare earth metals of 0.1 to 10 wt. %, wherein the yttrium content among the rare earth metal content proportion is 0.1 to 5.0 wt. %, a manganese proportion of 0.01 to 0.2 wt. %, an aluminium proportion of less than 0.1 wt. %, a proportion of copper, nickel and iron of less than 0.10 wt. % in each case, and a proportion of other physiologically undesirable impurities totaling less than 0.8 wt. %, wherein the remainder of the alloy is magnesium up to 100 wt. %.