Different means of introduction of the finite disturbance propagation velocity while the gradient dependences including in heat- and mass transfer theory are presented. The model of diffusion with finite velocity makes it possible to reveal the mechanism of molecular susceptibility to the local concentration distribution. The finite velocity of heart transfer is provided including the relaxation time in Fourier law. In fluid mechanics Maxwell body as a reologic model of viscoelastic medium leads to hyperbolic hydrodynamic equations, containing disturbance propagation velocity equal to sound velocity.