Aperiodic crystals which are long range ordered materials present original dynamics features due to the lack of translational symmetry formally implying the nonvalidity of the Brillouin zone concept. This Letter reports the observation by neutron scattering of an overdamped acousticlike mode at a Bragg peak position in a n-alkane–urea inclusion crystal. This result implies the existence of a gap in the dispersion branch. The gap and anomalous damping of these collective modes are discussed in terms of specific dynamics and interaction in aperiodic materials.