A magnetoplasma made up of a background of isotropic electrons and protons and a beam of anisotropic electrons (T⊥/T∥>1), with drift velocity parallel to the ambient magnetic field, can feed different unstable modes. Numerical solution of the dispersion equation in the wavenumber plane (k∥,k⊥) reveals several unstable modes with islets of oblique growth unconnected to the unstable parallel modes. The mechanisms involved in the growth and saturation of the fastest instability do not necessarily exclude later developments of other instabilities. Competing processes among the coexisting unstable waves are expected. Linear analysis or one-dimensional computer simulations cannot properly address this problem; there would not be interaction of modes propagating at different angles to the static magnetic field. Linear and nonlinear evolutions of the modes are studied via computer simulation with a two-dimensional particle code (KEMPO2). Results show that several modes are excited with different timescales. Some modes are only temporarily excited, while others persist in the system. The distribution function is significantly changed by the first excited modes, the beam-mode waves. In later stages of development, forward and backward oblique whistler mode waves are excited. A final stage is characterized by coexistence of several waves with different frequencies and wavelengths. The beam-mode waves have frequencies close to the plasma frequency, whereas the frequencies of the whistler mode waves fall near a half of the cyclotron frequency. These results may be relevant to the interpretation of wave activities observed in the Earth's magnetosphere by the GEOS 1, GEOS 2, and GEOTAIL satellites or in the Uranian bow shock by Voyager 2. ¿ American Geophysical Union 1996