Mg isotopic anomalies were determined on inclusions in the Allende meteorite. Measured Mg isotopic ratios were corrected for mass fractionation by normalizing to the terrestrial (normal) 25Mg/24Mg. Relative to normal Mg, Allende samples show distinct isotopic anomalies which correspond to enrichment of 24Mg or 26Mg of up to 3 per mil or depletion of 25Mg of up to 1.5 per mil. One sample shows a depletion of 24Mg or 26Mg by 1.7 per mil or an enrichment of 25Mg by 0.85 per mil. These anomalies are smaller by a factor of ten than found for the oxygen isotopes. Samples with large oxygen effects (up to 5%) yield normal Mg indicating a lack of correlation between the O and Mg effects. A Ca-Al rich chondrule with primitive 87Sr/86Sr and normal 84Sr/86Sr has a significant Mg anomaly. The Mg anomalies do not correlate with Al/Mg and do not appear to be due to 26Al decay. The anomaly in the only sample depleted in 26Mg cannot be due to 26Al decay. The isotopic composition of Mg in a sample of the total meteorite is normal. These results accentuate the important character of Allende inclusions but do not uniquely identify the nuclear processes responsible for the Mg and O effects.