  We present a systematic construction of integrable third order systems based
on the coupling of an integrable second order equation and a Riccati equation.
This approach is the extension of the Gambier method that led to the equation
that bears his name. Our study is carried through for both continuous and
discrete systems. In both cases the investigation is based on the study of the
singularities of the system (the Painlev\'e method for ODE's and the
singularity confinement method for mappings).
