The magnesium isotopic composition of some extraterrestrial dust particles has been measured. The particles are believed to be samples of interplanetary dust, a significant fraction of which originated from the disaggregation of comets and may contain preserved isotopic anomalies. Improvements in mass spectrometric and sample preparation techniques have made it possible to measure the magnesium isotopic composition of the dust particles, which are typically 10 micrometers in size and contain on the order of 10(-10) gram of magnesium. Of the 13 samples analyzed, nine have the terrestrial magnesium isotopic composition within 2 parts per thousand, and one shows isotopic mass fractionation of 1.1 percent per mass unit. A subset of the particles, described as chondritic aggregates, are very close to normal isotopic composition, but their normalized isotopic ratios appear to show nonlinear effects of 3 to 4 parts per thousand, which is near the present limit of detection for samples of this size. The isotopic composition of calcium was also determined in one particle and found to be normal within 2 percent. It is clear that the isotopic composition of interplanetary dust particles can be determined with good precision. Collection of dust particles during the earth's passage through a comet tail or an intense meteor stream may permit laboratory analysis of material from a known comet.