The frequency distributions of spectral lines of nonhydrogenic atoms broadened by local fields of both electrons and ions in a plasma are calculated in the classical path approximation. The electron collisions are treated by an impact theory which takes into account deviations from adiabaticity. For the ion effects, the adiabatic approximation can be used to describe the time-dependent wave functions. The various approximations employed were examined for self-consistency, and an accuracy of about 20% in the resulting line profiles is expected. Good agreement with Wulff's experimental helium line profiles was obtained while there are large deviations from the adiabatic theory, especially for the line shifts. Asymptotic distributions for the line wings are given for astrophysical applications. Here the ion effects can be as important as the electron effects and lead to large asymmetries, but near the line core electrons usually dominate. Numerical results are tabulated for 24 neutral helium lines with principal quantum numbers up to five.