  We investigate the dynamics of Eulerian walkers as a model of self-organized
criticality. The evolution of the system is subdivided into characteristic
periods which can be seen as avalanches. The structure of avalanches is
described and the critical exponent in the distribution of first avalanches
$\tau=2$ is determined. We also study a mean square displacement of Eulerian
walkers and obtain a simple diffusion law in the critical state. The evolution
of underlying medium from a random state to the critical one is also described.
