Summary: We introduce the notions of pairwise \(m\)-dependence and blockwise and pairwise \(m\)-dependence of random variables \(\{X_n,n\geq 1\}\). For a sequence of blockwise and pairwise \(m\)-dependent random variables \(\{X_n,n\geq 1\}\), we provide conditions for \((\sum^n_{j=1} (X_j-EX_j))/n^{1/r}\to 0\) a.s. as \(n\to\infty\) \((1\leq r<2)\). We also establish the strong law of large numbers for sequences of pairwise \(m\)-dependent random variables.