The rolling resistance and the effective radius of a vehicle's tyre are two important characteristics that affect its dynamics, performances and comfort. Thanks to their dependence on tyre inflation pressure, the online estimation of such parameters could be used to monitor tyre pressures using an indirect approach. By considering rotational and longitudinal dynamics models, this paper proposes to apply observers for this online estimation using measurements of wheel angular velocities and engine torque. These latter signals being available on major vehicle Controller Area Networks (CAN), the proposed solutions do not require additional sensors. These nonlinear observers are based, first, on high gain approach, and then on high order sliding mode approach allowing robustness and finite time convergence. The originality of the presented results consists in providing a joint estimation of both variables, wheel effective radius and rolling resistance force. The observers offer the very-first solution for dynamical estimation of rolling resistance in standard driving conditions, the rolling resistance being very difficult to estimate by an online procedure. Simulations and experimental results allow to discuss the effect of tyre pressure on these parameters and to illustrate the applicability of the proposed approach.