Let [Formula: see text] be a non-commutative semiring with [Formula: see text]. We study the notions of 2-absorbing and strong 2-absorbing ideals of [Formula: see text] and we show that if the semiring is commutative, then these two notions are the same. Also, we give an example to show that in general, these two notions are different. Many properties of (strong) 2-absorbing ideals are proved as a generalization to the results for those over rings. For example, we show that a proper subtractive ideal [Formula: see text] of a semiring [Formula: see text] is a 2-absorbing ideal of [Formula: see text] if and only if whenever [Formula: see text], [Formula: see text] and [Formula: see text] are left ideals of [Formula: see text] such that [Formula: see text], then [Formula: see text] or [Formula: see text] or [Formula: see text].