We examine whether observable Majoron emission in double beta decay can be compatible with big-bang nucleosynthesis (NS) and the observed neutrino flux from SN 1987A. It is found that the NS upper bound on He-4 abundance implies that the Majoron-neutrino Yukawa coupling constant g less-than-or-equal-to 9 X 10(-6) and its maximal value is allowed only when the scalar quartic coupling constant lambda is extremely small, lambda less-than-or-equal-to 100g2. It is also observed that, although quite less restrictive, SN 1987A also provides independent constraints on coupling constants.