The character and role of finite correlations between potential and magnetic low-frequency plasma excitations are investigated. Caused by the Lorentz force, they are significantly inherent to the nonlinear plasma behaviour. The cross-field correlations are found to narrow the renormalized width of the potential fluctuation spectrum and broaden that of the magnetic one. So the anomalous diffusion relevant to the long-wave perturbations, is increased. The anomalous heat conductivity associated with the short-wave motions, is not essentially influenced.