  The absolute continuity of the spectrum for the periodic Dirac operator $$
\hat D=\sum_{j=1}^n(-i\frac {\partial}{\partial x_j}-A_j)\hat \alpha_j + \hat
V^{(0)}+\hat V^{(1)}, x\in R^n, n\geq 3, $$ is proved given that either $A\in
C(R^n;R^n)\cap H^q_{loc}(R^n;R^n)$, 2q > n-2, or the Fourier series of the
vector potential $A:R^n\to R^n$ is absolutely convergent. Here, $\hat
V^{(s)}=(\hat V^{(s)})^*$ are continuous matrix functions and $\hat V^{(s)}\hat
\alpha_j=(-1}^s\hat \alpha_j\hat V^{(s)}$ for all anticommuting Hermitian
matrices $\hat \alpha_j$, $\hat \alpha_j^2=\hat I$, s=0,1.
