The well-known Tichonovís theorem for quasi-stationary approximation of two-time-scaled dynamical systems is applied to a mathematical model of the influence of Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway. On the basis of previously determined parameters, the eleven ordinary differential equations of the model are written in dimensionless form and their terms are evaluated. In accordance with the terminology of the Tichonovís theorem, it is established that four of the variables are fast varying and the corresponding kinetic equations form an attached system. The other seven variables are slow varying and their kinetic equations form a degenerated system. It is shown that two equations of the degenerated system are independent of the other five and are conjugated to form a strongly damped linear oscillator (damper). The five variables are dependent on the variables of the damper. In this way, the two-component reaction between Raf-1*/RKIP/ ERK-PP and RKIP-P/RP protein complexes is identified to play a role of a driver of the signalling pathway behaviour.