The (1-x)Bi0.5Na0.5TiO3–xBaTiO3 (BNT-xBT) system with composition at its morphotropic phase boundary (MPB) has received significant attention because of their attractive properties as lead-free piezoceramics. Although the basic properties of this system are well-established, reports about the stability of the functional properties of these piezoelectric materials are still lacking. A study on the dielectric and piezoelectric properties of BNT-xBT close to their MPB, with emphasis on material response under high electric field or mechanical stress, is performed in this work. The results indicate that the BNT-BT system exhibits a high stability of dielectric and piezoelectric properties, making it potentially interesting for specific applications. A direct correlation between piezoelectric properties and nonlinear response is evidenced for a wide number of piezoceramics, which is expected due to the extrinsic nature of the piezoelectric response. Finding compositions that show high electromechanical properties and low nonlinear behavior is a challenge in the search for competitive lead-free piezoceramics.