Diamagnetism in helium Rydberg atoms is studied near the ionisation threshold using constant scaled-energy laser spectroscopy. Quasi-Landau resonances in the Fouriertransform of the energy spectrum are explained using the classical periodic-orbit theory. Longlaser scans combined with a high-frequency resolution allow for a detailed comparison betweenexperiment and theory. Resonances with a scaled action Stup to 20 are identified andreproduced with an accuracy of 0.015. It is demonstrated that interference effects betweenresonances should be taken into account. © 1993 IOP Publishing Ltd.