ABSTRACT.In the present paper, we introduce the notion of \( (\Phi, \Psi) \)-neutrosophic subsemigroups of a semigroup where \( \Phi, \Psi \in \{\in, q, \in \vee q\} \), and related properties are investigated. We consider characterizations of an \( (\in, \in) \)-neutrosophic subsemigroup and an \( (\in, \in \vee q) \)-neutrosophic subsemigroup. Conditions for the neutrosophic \( \varepsilon \)-subsets, neutrosophic \( q \)-subsets and neutrosophic \( \in \vee q \)-subsets to be subsemigroups are discussed. Finally, we discuss conditions for a neutrosophic set to be a \( (q, \in \vee q) \)-neutrosophic subsemigroup.