Summary: Let \(R\) be a commutative ring with \(1\neq 0\). We recall that a proper ideal \(I\) of \(R\) is called a weakly 2-absorbing primary ideal of \(R\) if whenever \(a,b,c\in R\) and \(0\not=abc\in I\), then \(ab\in I\) or \(ac\in\sqrt{I}\) or \(bc\in\sqrt{I}\). In this paper, we introduce a new class of ideals that is closely related to the class of weakly 2-absorbing primary ideals. Let \(I(R)\) be the set of all ideals of \(R\) and let \(\delta:I(R)\rightarrow I(R)\) be a function. Then \(\delta\) is called an expansion function of ideals of \(R\) if whenever \(L,I,J\) are ideals of \(R\) with \(J\subseteq I\), then \(L\subseteq\delta(L)\) and \(\delta(J)\subseteq\delta(I)\). Let \(\delta\) be an expansion function of ideals of \(R\). Then a proper ideal \(I\) of \(R\) (i.e., \(I\not=R)\) is called a weakly 2-absorbing \(\delta \)-primary ideal if \(0\not=abc\in I\) implies \(ab\in I\) or \(ac\in\delta(I)\) or \(bc\in\delta(I)\). For example, let \(\delta:I(R)\rightarrow I(R)\) such that \(\delta(I)=\sqrt{I}\). Then \(\delta\) is an expansion function of ideals of \(R\), and hence a proper ideal \(I\) of \(R\) is a weakly 2-absorbing primary ideal of \(R\) if and only if \(I\) is a weakly 2-absorbing \(\delta\)-primary ideal of \(R\). A number of results concerning weakly 2-absorbing \(\delta\)-primary ideals and examples of weakly 2-absorbing \(\delta\)-primary ideals are given.