This paper proposes two speed observers for high-performance induction machine drives, both adopting an online adaptation law based on a new total least-squares (TLS) technique: the TLS EXIN neuron. The first is a model reference adaptive system (MRAS) observer with a neural adaptive integrator in the reference model and a neural adaptive model trained online by the TLS EXIN neuron. This observer, presented in a previous article of the authors, has been improved here in two aspects: first, the neural adaptive integrator has been modified to make its learning factor vary according to the reference speed of the drive, second, a neural adaptive model based on the modified Euler integration has been proposed to solve the discretization instability problem in field-weakening. The second observer is a new full-order adaptive one based 'on the state equations of the induction machine, where the speed is estimated by means of a TLS EXIN adaptation technique. Both these observers have been provided with an inverter nonlinearity'compensation algorithm and with techniques for the online estimation of the stator resistance of the machine. Moreover, a thorough theoretical stability analysis has been developed for them both, with particular reference to the field-weakening region behavior for the TLS MRAS observer and to the regenerating mode at low speeds for the TLS adaptive observer. Both speed observers have been verified in numerical simulation and experimentally on a test setup, and have also been compared experimentally with the BPN MRAS observer, the classic adaptive observer and with an open-loop estimator. Results show that both proposed observers outperform all other three observers in every working condition, with the TLS adaptive observer resulting in a better performance than the TLS MRAS observer.