If a system with regular system pencil and relative degree greater than one is perturbed, the relative degree will typically decrease, and new finite zeros will appear. These new zeros are singularly perturbed. This paper applies a new canonical parameterization to systems with singular system pencils. Such systems have undefined relative degree. In singular systems, new zeros also appear under small perturbation, but they are not necessarily singularly perturbed. Rather, these zeros may appear at any frequency.