23 pages ; International audience ; We study the non-equilibrium transport properties of fully (exactly) screened Kondo quantum dots subject to a finite bias voltage or a finite temperature. Firstly, we calculate the Fermi-liquid coefficients of the conductance for models with arbitrary spin, i.e. its leading behaviour for small bias voltages or temperatures. Secondly, we determine the low-temperature behaviour of the static susceptibility from the exactly known Bethe Ansatz results for the magnetisation. Thirdly, we study the crossover from strong to weak coupling in the spin-1/2 and the spin-1 models coupled to one or two screening channels respectively. Using a real-time renormalisation group method we calculate the static and dynamical spin-spin correlation functions for the spin-1/2 model as well as the linear and differential conductance and the static susceptibility for the spin-1 model. We define various Kondo scales and discuss their relations. We assess the validity of the renormalisation-group treatment by comparing with known results for the temperature dependence of the linear conductance and static susceptibility as well as the Fermi-liquid behaviour at low energies.