Bosbach states and Riečan states are two different types of many-valued generalizations of classical probability measures on Boolean algebras by extending the prominent Kolmogorov axioms in different ways.Being regarded as algebraic and axiomatic counterparts of the semantic quantification in probabilistically quantitative logic, both states draw great interests of researchers in the community of non-classical mathematical logics.It has been proved in the literature that Bosbach states and Riečan states coincide on many-valued logical algebras having the Glivenko property, and that the Glivenko property plays a key role in the study of construction and existence of states on logical algebras.This paper studies the Glivenko property of NMG-algebras with respect to a nucleus, providing several necessary and sufficient conditions for the underlying nucleus to be a homomorphism into the NMG-algebra with its range as the supporting set.A particularly interesting characterization shows that a nucleus on an NMG-algebra is such a homomorphism if and only if it is a double relative negation defined by an involutive element whose (canonical) negation is a fixpoint of the t-norm square operation.