We have made 2 mm continuum observations of 15 bright-rimmed clouds (BRCs) associated with IRAS point sources and S140 with the Nobeyama Bolometer Array (NOBA) mounted on the 45 m telescope of Nobeyama Radio Observatory. Continuum emission was detected in five BRCs and in S140. These five BRCs are known to be associated with near-infrared YSO clusters, mostly on the side facing toward the exciting star(s) and, therefore, are likely the sites of small-scale sequential star formation. The detected emission peaks of these five sources correspond to the IRAS positions within the positional errors, and the IRAS sources are considered to be protostars (Class 0/I-like sources) that were formed most recently in the BRCs. Four of them are clearly extended more than the telescope beam, suggesting the presence of circumstellar structures. The circumstellar masses derived from the 2 mm continuum are ~5–90 M, which are more massive than those of the nearby Class 0/I objects (1 M). This fact and the relatively large bolometric luminosities of these objects suggest that the mass of the cluster or star(s) most recently formed in these BRCs could be higher than those of the previously formed stars found in the near-infrared cluster. The comparisons with previous observations of Bok globules unassociated with bright rims and other objects are discussed. Most noteworthy is that the ratios of the bolometric luminosity to the circumstellar mass are significantly higher for these BRCs than for Bok globules.