  Nonlinear coherent modes are the collective states of trapped Bose atoms,
corresponding to different energy levels. These modes can be created starting
from the ground state condensate that can be excited by means of a resonant
alternating field. A thorough theory for the resonant excitation of the
coherent modes is presented. The necessary and sufficient conditions for the
feasibility of this process are found. Temporal behaviour of fractional
populations and of relative phases exhibits dynamic critical phenomena on a
critical line of the parametric manifold. The origin of these critical
phenomena is elucidated by analyzing the structure of the phase space. An
atomic cloud, containing the coherent modes, possesses several interesting
features, such as interference patterns, interference current, spin squeezing,
and massive entanglement. The developed theory suggests a generalization of
resonant effects in optics to nonlinear systems of Bose-condensed atoms.
