Abstract Mathematical modelling of biological, ecological or sociological systems leads very often to systems of nonlinear ordinary differential equations exhibiting time hierarchy. Analysis of this hierarchy helps to overcome the difficulties in their solution. In the simplest case it consists of separating the equations into two sybsystems-called slow and fast - so that the equations with left sides multiplied by a small parameter e are gathered in the fast one. Solutions of such systems may be sometimes approximated by solutions of the adjoint degenerated system which arises from the original system as e converges towards zero. Conditions for such approximation are specified by the theorem of Tikhonov. They exclude an approximation of the original solution when the fast subsystem has no one-point stable attractor. In the paper this limitation is removed by presenting an extension of the theorem of Tikhonov, which allows the approximate solution of the slow subsystem even when the dynamics of the fast subsystem exhibits a general C 2 -attractor. The applicability of this approach is illustrated by an example of the system exhibiting a limit cycle.