Summary: For any positive integers \(l\) and \(m\), a set of integers is said to be (weakly) \(l\)-sum-free modulo \(m\) if it contains no (pairwise distinct) elements \(x_1,x_2,\ldots,x_l,y\) satisfying the congruence \(x_1+\ldots+x_l\equiv y\bmod{m}\). It is proved that, for any positive integers \(k\) and \(l\), there exists a largest integer \(n\) for which the set of the first \(n\) positive integers \(\{1,2,\ldots,n\}\) admits a partition into \(k\) (weakly) \(l\)-sum-free sets modulo \(m\). This number is called the generalized (weak) Schur number modulo \(m\), associated with \(k\) and \(l\). In this paper, for all positive integers \(k\) and \(l\), the exact value of these modular Schur numbers are determined for \(m=1, 2\) and 3.