Let $R$ be a commutative semiring. We define a proper ideal $I$ of $R$ to be 2-absorbing (resp., weakly 2-absorbing) if $abc{in}I$ (resp., $0{ eq}abc{in}I$) implies $ab{in}I$ or $ac{in}I$ or $bc{in}I$. We show that a weakly 2-absorbing ideal $I$ with $I^3{ eq}0$ is 2-absorbing. We give a number of results concerning 2-absorbing and weakly 2-absorbing ideals and examples of weakly 2-absorbing ideals. Finally we de ne the concept of 0 - (1-, 2-, 3-)2-absorbing ideals of $R$ and study the relationship among these classes of ideals of $R$.