Low dimensional magnetic structures show interesting and novel phenomena such as oscillatory magnetic coupling and giant magnetoresistance. Magnetic second harmonic generation (MSHG) can provide unique information on magnetic surfaces and interfaces because, within the dipole approximation, broken space-inversion symmetry at the surface or interface of centrosymmetric media, and broken time-reversal symmetry arising from the magnetization, are both required in order to observe a magnetic-field-dependent second harmonic response. However, the additional reduction in symmetry arising from the magetization produces many non-zero susceptibility tensor components, particularly in the case of vicinal, stepped surfaces of 1m symmetry, and care is needed in designing experiments that will produce readily interpretable results. Phenomenological expressions for the MSHG response from systems of 1m symmetry are presented, where combinations of input and output polarizations and magnetic field orientations allow the essential physics of these systems to be explored, particularly in relation to distinguishing terrace and step contributions to the magnetization from vicinal surfaces and interfaces. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)