  The model of self-organizing Eulerian walkers is numerically investigated on
the square lattice. The critical exponents for the distribution of a number of
steps ($\tau_l$) and visited sites ($\tau_s$) characterizing the process of
transformation from one recurrent configuration to another are calculated using
the finite-size scaling analysis. Two different kinds of dynamical rules are
considered. The results of simulations show that both the versions of the model
belong to the same class of universality with the critical exponents
$\tau_l=\tau_s=1.75\pm 0.1$.
