This article introduces the concept of gap-singularities to underline particular phenomena related to the choice of the outputs in some non-linear systems. It is shown that, when bounds on the variables are considered, this property induces a topological isolation of the gap-singular trajectories in the outputs domain. In the context of differentially flat systems, a procedure to detect gap-singularities is provided because it is related to the existence of a singularity of flatness. The examples that are presented in this article show that taking gap-singularities into account can improve some trajectory planning algorithms based on an optimal control approach like in the Nonlinear Trajectory Generation software.