  We identify a non-local symmetry for Yang-Mills theories in 1+1 and 2+1
spacetime dimensions. The symmetry mixes a vector current with the gauge field.
The current involved in the symmetry is required to satisfy certain
constraints. The explicit solution for the current obeying these constraints,
is obtained in two spacetime dimensions and in the abelian case in three
dimensions. We conjecture that the current is generated from a non-local gauge
and Lorentz invariant mass term in three dimensions and provide some evidence
for it.
  We also posit a conserved current associated with the symmetry generators and
derive some of its properties. In the Abelian case, we compute the symmetry
algebra and show that additional symmetry generators have to be included for
the algebra to close. The algebra contains an SO(2,1) subalgebra. We also
comment on the implications of this symmetry for N=1 supersymmetry.
