Abstract SECOND approximation equations are derived from a simple quasilinear hypothetical model of a viscous fluid. The model is obtained by introducing supplementary non-linear terms into the expressions for the deformation rate tensor components. The defining equation retains its classical linear tensorial form. The model is suggested by the analogy between the vortex equation in hydrodynamics and the equation of induction in magnetohydrodynamics. A method for determining the physical parameter in the proposed equations experimentally is outlined. As an example, we consider the behaviour of perturbations in the flow of a viscous incompressible fluid possessing “transverse fluidity”.