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A spectroscopic study of Rydberg states of helium ($n$ = 30 and 45) inmagnetic, electric and combined magnetic and electric fields with arbitraryrelative orientations of the field vectors is presented. The emphasis is on twospecial cases where (i) the diamagnetic term is negligible and bothparamagnetic Zeeman and Stark effects are linear ($n$ = 30, $B \leq$ 120 mT and$F$ = 0 - 78 V/cm ), and (ii) the diamagnetic term is dominant and the Starkeffect is linear ($n$ = 45, $B$ = 277 mT and $F$ = 0 - 8 V/cm). Both casescorrespond to regimes where the interactions induced by the electric andmagnetic fields are much weaker than the Coulomb interaction, but much strongerthan the spin-orbit interaction. The experimental spectra are compared tospectra calculated by determining the eigenvalues of the Hamiltonian matrixdescribing helium Rydberg states in the external fields. The spectra and thecalculated energy-level diagrams in external fields reveal avoided crossingsbetween levels of different $m_l$ values and pronounced $m_l$-mixing effects atall angles between the electric and magnetic field vectors other than 0. Theseobservations are discussed in the context of the development of a method togenerate dense samples of cold atoms and molecules in a magnetic trap followingRydberg-Stark deceleration.

Rydberg states of helium in electric and magnetic fields of arbitrary relative orientation