We show that the pair (rotor position, resistance) of a nonsalient permanent magnet synchronous motor (PMSM) is not observable in the sensorless setting, namely, when only the electrical signals (voltages and intensities) are measured. However, if the rotation speed omega and the current in rotating frame i(d) are not constantly zero, we prove that there only exist a maximum of six indistinguishable solutions, the resistance being the root of a polynomial of degree six. Besides, in the particular case where omega, i(d), and i(q) are constant, we show that the number of possible solutions is reduced to two, with two well-identified possible values for the resistance. Those two solutions can be dissociated if the sign of i(q) (namely, the mode of use of the motor) is known. Inspired by the nonlinear Luenberger methodology, this property enables us to propose an estimation algorithm, which relies on a one-dimensional minimization of a criterion involving the voltages and intensities filtered at three distinct sufficiently large frequencies. Its performances are tested and illustrated in simulations on real data.