A comprehensive micro-macroscopic model of the continuous hardening of 3d-axisymmetric steel components by induction heating has been developed. At the macroscopic scale, the Maxwell and heat flow equations are solved using a mixed numerical formulation : the inductor and the workpiece are enmeshed with finite elements (FE) but boundary elements (BE) are used for the solution of the electromagnetic equations in the ambient air. This method allows the inductor to be moved with respect to the workpiece without any remeshing procedure. The heat flow equation is solved for the workpiece using the same FE mesh. For the thermal boundary conditions, a net radiation method has been implemented to account for grey diffuse bodies and the viewing factors of the element facets are calculated using a ''shooting'' technique. The boundary condition associated with the water spraying below the inductor is deduced,from the inverse modelling of temperatures measured at various locations of a test piece. These macroscopic calculations of induction heating have been coupled to a microscopic model describing the solid state transformations that occur during both heating and cooling. From the local thermal history, the evolutions of the various phase fractions are predicted from TTT-diagrams using an additivity principle. A micro-enthalpy method has been implemented in the heat flow calculations in order to account for the latent heat released by the various transformations. At each time step the local properties of the material, in particular its magnetic susceptibility, are updated according to the new temperatures and magnetic field. The results of the simulation are compared with experimental cooling curves and hardness profiles.