The evolution of nonlinear electron plasma waves in weakly magnetized
plasmas is studied for conditions where the principal waves propagate
along the magnetic held lines. The analysis is based on an electrostat
ic fluid model for the waves. Numerical results using a spectral metho
d with periodic boundary conditions demonstrate ''quasi-collapsing'' s
olutions for localized initial conditions with sufficiently high ampli
tude. The possibility of acceleration of electrons by the high-frequen
cy waves is discussed. It is demonstrated that electrons are likely to
gain energy in parts of the nonlinear wavepacket and to loose all, or
most of, this energy again in other parts.