  One dimensional Dirac operators $$ L_{bc}(v) y = i 1 & 0 0 & -1 \frac{dy}{dx}
+ v(x) y, \quad y = y_1 y_2, \quad x\in[0,\pi]$$, considered with
$L^2$-potentials $ v(x) = 0 & P(x) Q(x) & 0$ and subject to regular boundary
conditions ($bc$), have discrete spectrum. For strictly regular $bc,$ the
spectrum of the free operator $ L_{bc}(0) $ is simple while the spectrum of $
L_{bc}(v) $ is eventually simple, and the corresponding normalized root
function systems are Riesz bases. For expansions of functions of bounded
variation about these Riesz bases, we prove the uniform equiconvergence
property and point-wise convergence on the closed interval $[0,\pi].$ Analogous
results are obtained for regular but not strictly regular $bc.$
