The dust properties in the Large and Small Magellanic Clouds are studied using the HERITAGE Herschel Key Project photometric data in five bands from 100 to 500 µm . Three simple models of dust emission were fit to the observations : a single temperature blackbody modified by a power-law emissivity ( SMBB ) , a single temperature blackbody modified by a broken power-law emissivity ( BEMBB ) , and two blackbodies with different temperatures , both modified by the same power-law emissivity ( TTMBB ) . Using these models we investigate the origin of the submm excess ; defined as the submillimeter ( submm ) emission above that expected from SMBB models fit to observations < 200 \micron . We find that the BEMBB model produces the lowest fit residuals with pixel-averaged 500 µm submm excesses of 27 % and 43 % for the LMC and SMC , respectively . Adopting gas masses from previous works , the gas-to-dust ratios calculated from our the fitting results shows that the TTMBB fits require significantly more dust than are available even if all the metals present in the interstellar medium ( ISM ) were condensed into dust . This indicates that the submm excess is more likely to be due to emissivity variations than a second population of colder dust . We derive integrated dust masses of ( 7.3 \pm 1.7 ) \times 10 ^ { 5 } and ( 8.3 \pm 2.1 ) \times 10 ^ { 4 }  M _ { \sun } for the LMC and SMC , respectively . We find significant correlations between the submm excess and other dust properties ; further work is needed to determine the relative contributions of fitting noise and ISM physics to the correlations .