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(Abridged) An anisotropic theory of MHD turbulence with nonvanishingcross-helicity is constructed based on Boldyrev's alignment hypothesis andprobabilities p and q for fluctuations v and b to be positively or negativelyaligned. Guided by observations suggesting that the normalized cross-helicityand the probability p are approximately constant in the inertial range, ageneralization of Boldyrev's theory is derived that depends on the three ratiosw+/w-, epsilon+/epsilon-, and p/q. The theory reduces to Boldyrev's originaltheory when w+ = w-, epsilon+ = epsilon-, and p = q.

Theory of incompressible MHD turbulence with scale-dependent alignment and cross-helicity