Field studies have shown that mineral dust particles can act as ice nuclei in cirrus clouds. Here, we present a laboratory investigation of heterogeneous ice nucleation on surrogates of mineral dust particles, in particular pure Arizona test dust (ATD) particles, and ATD particles coated with sulfuric acid. The experiments have been performed using a new apparatus in which ice formation on the particles is determined by optical microscopy at temperatures between 197 and 260 K and relative humidities up to water saturation. The experiments reveal that pure and sulfuric acid coated ATD particles nucleate ice at considerably lower relative humidities than required for homogeneous ice nucleation in liquid aerosols. Nucleation occurred over a broad relative humidity range indicating that the different minerals contained in ATD have different ice nucleation thresholds. No significant difference in the ice nucleation ability of pure and H2SO4 coated ATD particles was observed. Below 240 K, ice nucleated on ATD particles apparently by deposition nucleation. Preactivation of ATD particles, that is, a reduction in supersaturation, required for heterogeneous ice nucleation after a previous ice nucleation event on the same particle, has been observed for temperatures as low as 200 K. Differences of 10--30% in the onset RHice values were obtained for particles with or without preactivation. The results indicate that pure and sulfuric acid coated mineral dust particles may act as efficient ice nuclei in the atmosphere. Preactivation of the particles should be considered when modeling long-range transport of mineral dust particles and their impact on cloud formation.