In this paper, we begin with the definition of the $S$-resolvent set of a linear relation. Throughout this paper, $X$ will denote a normed linear space over the complex field $\mathbb{C}$. Operator $S$ plays the role of a transition multivalued linear operator from $X$. It is the main goal of the present note to study the basic spectral properties of $T$ linked to the transition multivalued linear operator $S$.