Singular ordinary differential equations are another type of non-regular non-linear equations that are absent from economics textbooks. Singular equations are ordinary differential equations that can display, globally or locally, infinite speeds of propagation. Global speeds of propagation can be found in fast-slow equations, and constrained or impasse equations can display local infinite speeds of propagation. This chapter presents a brief introduction to the dynamics, explicit, and/or qualitative, of those two types of differential equations, and of singularity induced bifurcations. The type of singularities that occur in these equations can be quite frequent in macroeconomic dynamic models in which externalities or feedback effects generated by rules dominate the most common incentive mechanisms. Impasse singularities can be associated to the existence of temporary indeterminate macroeconomic equilibrium regimes.