Abstract: Homeomorphism helps us to determine the properties of complicated spaces easily. In this sequel, the aim of this short communication is introduce and study two new types of homeomorphisms, namely; pairwise s*g-homeomorphism and pairwise s*gc-homeomorphism in bitopological spaces. Here researchers proved that the set of all pairwise s*gc-homeomorphisms forms a group which contains the set of all pairwise homeomorphisms as a subgroup. Furthermore, the relationships between newly introduced and existing homeomorphisms are established.