<p>This paper is devoted to develop the concept of exceptional value for transcendental semigroups. First, we prove that exceptional set of a transcendental semigroup is the intersection of exceptional sets of the elements of the semigroup. A general idea to construct examples of transcendental semigroups having non-empty exceptional set is given here. We prove that the exceptional value of an abelian transcendental semigroup is same as the exceptional value for one of its generators. We give a circumstance related to the exceptional value in which the Julia set of the semigroup is connected. The location of the exceptional value of the semigroup, due to presence of Baker wandering domain is also investigated. Also, the concept of the exceptional set, in the context of conjugate transcendental semigroup is studied. Finally, we provide a necessary and sufficient condition on the conformal map to have the same exceptional set for conjugate semigroups.</p>