  A spectroscopic study of Rydberg states of helium ($n$ = 30 and 45) in
magnetic, electric and combined magnetic and electric fields with arbitrary
relative orientations of the field vectors is presented. The emphasis is on two
special cases where (i) the diamagnetic term is negligible and both
paramagnetic 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 Stark
effect is linear ($n$ = 45, $B$ = 277 mT and $F$ = 0 - 8 V/cm). Both cases
correspond to regimes where the interactions induced by the electric and
magnetic fields are much weaker than the Coulomb interaction, but much stronger
than the spin-orbit interaction. The experimental spectra are compared to
spectra calculated by determining the eigenvalues of the Hamiltonian matrix
describing helium Rydberg states in the external fields. The spectra and the
calculated energy-level diagrams in external fields reveal avoided crossings
between levels of different $m_l$ values and pronounced $m_l$-mixing effects at
all angles between the electric and magnetic field vectors other than 0. These
observations are discussed in the context of the development of a method to
generate dense samples of cold atoms and molecules in a magnetic trap following
Rydberg-Stark deceleration.
