For an integer linear program, Gomory's corner relaxation is obtained by ignoring the nonnegativity of the basic variables in a tableau formulation. A classical result of Gomory and Johnson characterizes minimal cut-generating functions in terms of subadditivity, symmetry, and periodicity. In this talk, we consider the general case, where we do not relax the nonnegativity of the basic variables. We show that the Gomory-Johnson theorem still holds if we replace "periodicity" by the notion of "nondecreasing function with respect to nonnegative integral vectors". We also prove a 2-Slope Theorem for extreme cut-generating functions in our setting, in the spirit of the 2-Slope Theorem of Gomory and Johnson.