  Consider a compact oriented surface $S$ of genus $g \geq 0$ and $m \geq 0$
punctured. The train track complex of $S$ which is defined by Hamenst\"adt is a
1-complex whose vertices are isotopy classes of complete train tracks on $S$.
Hamenst\"adt shows that if $3g-3+m \geq 2$, the mapping class group acts
properly discontinuously and cocompactly on the train track complex. We will
prove corresponding results for the excluded case, namely when $S$ is a
once-punctured torus or a 4-punctured sphere. To work this out, we redefinition
of two complexes for these surfaces.
