The triple velocity, the pressure–velocity, and the scalar–scalar–velocity correlations in incompressible turbulent shear flows and in passive scalar fields are studied by using the two-scale direct-interaction approximation, which satisfies the solenoidal condition of the velocity fields and systematically introduces the cutoff wave numbers. As a result, we obtain their expressions of the gradient diffusion type involving the effect of cross-diffusion. The model constants in the obtained expressions for the triple velocity and the pressure–velocity correlations are close to the values used in the turbulence models. The derived expression for the scalar–scalar–velocity correlation shows the complex dependence on the ratioRof the velocity length scale to the scalar one. As a special case ofR=1,we obtain its explicit expression whose model constant also agrees well with the numerically optimized value. ©1998 American Institute of Physics.