Abstract
For supersymmetric gauge theories with eight supercharges in four, five and six dimensions, a conserved current belongs to the linear multiplet. In the case of sixdimensional N = 1 , 0 $$ \mathcal{N}=\left(1,\ 0\right) $$ Poincaré supersymmetry, we present a consistent deformation of the linear multiplet which describes chiral anomalies. This is achieved by developing a superform formulation for the deformed linear multiplet. In the abelian case, we compute a nonlocal effective action generating the gauge anomaly.