The effect of the so-called local field terms of the dipolar interactions on the transverse relaxation of deuteron spin systems is investigated for a variety of physical situations. It is shown that the response of the spin systems to arbitrary pulse sequences can be calculated in an operator formalism. For illustration, calculations of the signals following a quadrupolar echo sequence are performed, and expressions for the echo amplitude are given including that for a system of a deuteron coupled to an arbitrary number of spins. A simple model is formulated and the transverse relaxation rate in supercooled liquids is calculated for the whole range of motional correlation times of experimental interest.