Discussed are ±m modes and ±m resonances of Dirac operators with vector potentials HA = α · (D - A(x)) + mβ. Asymptotic limits of ±m modes at infinity are derived when |A(x)| ≤ C〈x〉-ρ, ρ > 1, provided that HA has ±m modes. In wider classes of vector potentials, sparseness of the vector potentials which give rise to the ±m modes of HA are established. It is proved that no HA has ±m resonances if |A(x)| ≤ C〈x〉-ρ, ρ > 3/2. © 2011 World Scientific Publishing Company.