Generally, continuum theories of materials with damage treat the damage as an internal state variable, a variable whose evolution is governed by a rate‐type law. There is quite ample precedent, however, to treat such a quantity as governed instead by an equation of balance in addition to the conventional ones for mass, momentum, energy, and entropy. Here, we present a theory of this type. As a first test of the theory, we solve the problem of one‐dimensional creep. We assume homogeneous motion and thus obtain an ordinary differential equation for the damage. This equation is complicated enough so that the exact solution is not directly useful. Of course, a numerical solution would be easy to carry out, but it would have to be done with extreme care so as to ensure that appropriate ranges of the variables are considered to include all possible types of behavior of the equation. We use the qualitative theory of ordinary differential equations to study exhaustively the evolution of the damage. This leads to precise and natural definitions of material stability and instability. After that, we present representative numerical solutions for evolution of damage and strain. An interesting outcome is that there are some solutions which are welll behaved for a finite length of time, then fail to exist. Such solutions clearly imply the onset of localization of deformation.