The use of SO and SO2 as probes of the dense interstellar medium in the nearby starburst galaxies NGC 253 and M82 is described. Emission in the 99.3 GHz 3(2) - 2(1) rotational transition of SO was detected in NGC 253 and possibly in M82, and upper limits are reported for emission in the 219.9 GHz 6(5) - 5(4) transition of SO and two lines of SO2. The column density of SO relative to carbon sulfide, CS, is more than 0.08 in NGC 253, a value not much lower than Galactic ratios and consistent with models of dense interstellar clouds with a fractional abundance of atomic oxgyen greater than about 10 exp -7. The 218.8 GHz 3(21) - 2(20) transition of para-formaldehyde, with an excitation temperature of 68 K, was also detected in NGC 253.