Summary: Following Balas (1979) we generate cuts to solve disjunctive interval linear or linear fractional programs of the form: \(\text{Max } f(x)\) such that \(a< Ax< b\), \(x_k x_j= 0\), \(k\neq j\). \(f(x)\) is a linear or a linear fractional function. In case in addition to the interval and disjunctive constraints \(x_j\)’s are required to be integers cuts proposed by Balas (1979) and by Armstrong et al (1979) can be combined to generate implied cuts. A certain class of disjunctive integer nonlinear programming problem is also treated.