Ti(50-x)Zr38NbxTa8Sn4 high-entropy alloys with x = 0, 10, and 20 at.% were produced by vacuum arc melting in a high-purity argon atmosphere. The initial microstructures consisted of equiaxial bcc grains with sizes of 115 ± 30 µm, 250 ± 60 µm, and 280 ± 70 µm for the Ti30Nb20, Ti40Nb10, and Ti50Nb0 alloys, respectively. The Ti30Nb20 and Ti40Nb10 alloys showed untypical mechanical behavior with a short strain-hardening stage followed by a gradual decrease in flow stress after reaching the yield point. Although these two alloys had some inclination toward macroscopic strain localization, their tensile elongation was similar to that obtained in the Ti50Nb0 alloy, which had a more extended stage of uniform deformation. The differences were associated with distinct microstructures observed after deformation to fracture. The formation of dislocation bands and the activation of cross-slip at the microscale, as well as the appearance of kink bands at the mesoscale, can result in plastic instability. In contrast, a lamellar-like microstructure with parallel dislocation bands, such as the one observed in the Ti50Nb0 alloy, can ensure a more stable mechanical behavior. The developed alloys (Ti30Nb20 and Ti40Nb10) have properties that make them highly attractive for biomedical application due to a combination of very high yield strengths (1090 and 930 MPa, respectively), low Young’s moduli (~78 and ~69 GPa, respectively), reasonable ductility, and excellent biocompatibility.