Study of weak Alfvenic turbulence*

We report a study of weak incompressible magnetohydrodynamic turbulence in the presence of a strong guide magnetic field. Such turbulence consists of weakly interacting Alfven waves propagating in opposite directions along the guide field. We consider both balanced and imbalanced turbulence. The imbalanced case is the case when the energies of counter-propagating Alfven waves are unequal. In this case we discuss the role of the so-called ``condensate,'' that is, the nonlinear magnetic fluctuations at $k_\|=0$ on the spectrum and structure of turbulence.