  In this paper, we examine the problem of anomalies of the fermionic currents
in the context of the very special relativity (VSR). We consider the VSR
contributions to the triangle amplitude $\left\langle J_{5}^{\lambda} J^{\mu}
J^{\nu} \right\rangle $, which allows the evaluation of the vector and axial
Ward identities. Actually, we observe that the VSR nonlocal effects respect the
vector Ward identity, and it also contributes in a very interesting and unique
way for the Adler-Bell-Jackiw anomaly.
