The Goldreich-Sridhar model of incompressible turbulence provides us with an elegant approach to describing strong MHD turbulence. It relies on the fact that interacting Alfvenic waves are independent and have random polarization. However, in case of strong interaction, a spontaneous local axial asymmetry can arise. We used direct numerical simulations to show that polarization alignment occurs and that it grows larger at smaller scales. Assuming critical balance, this effect could lead to a shallower spectrum and stronger anisotropy. Even small changes in these two properties will have important astrophysical consequences, e. g., for the cosmic-ray physics.