This paper studies the estimation of the frictional torque of the synchromesh during the gear shifting operation in an electric vehicle equipped with a clutchless automated manual transmission (AMT). The clutchless drivetrain of the electric vehicle is discussed and the dynamical model of the powertrain from the electric traction motor to the synchromesh system of a two-speed AMT is developed. In order to estimate the frictional torque of the synchromesh, which is indeed an unknown input to the dynamical system, it is assumed to be generated by a fictitious autonomous system. Thereafter, the augmented state- space representation of the actual and fictitious state variables, which forms the basis for the observer design, is provided and the observability of this augmented system is discussed. A deterministic Luenberger observer and a stochastic Kalman-Bucy filter are designed in order to estimate the frictional torque of the synchromesh. The estimation is based on the measuring angular velocities of the electric motor and synchro ring together with the known electromagnetic torque of the traction motor. The performance of the observers is assessed experimentally by means of a test rig. The results demonstrate the satisfactory performance of the stochastic observer when the system encounters process and measurement noise which are likely to happen in practice.