  We describe the $(\alpha,\beta)$-metrics whose the $T$-tensor vanishes
($T$-condition) and the $(\alpha,\beta)$-metrics that satisfy the $\sigma
T$-condition $\sigma_hT^h_{ijk}=0$, where $\sigma_h=\frac{\partial
\sigma}{\partial x^h}$ and $\sigma$ is a smooth function on $M$. These classes
have already been obtained by Z. Shen and G. S. Asanov in a completely
different approach. The Finsler metrics of the first class are Berwaldian, the
metrics of the second class are almost regular non-Berwaldian Landsberg
metrics.
