This study compared the functional and physiological adaptations induced by concurrent training (CT) performed with repetitions to concentric failure and not to failure in elderly men. Fifty-two individuals (66.2 ± 5.2 years) completed the pre- and post-measurements and were divided into three groups: repetitions to failure (RFG, n = 17); repetitions not to failure (NFG, n = 20); and repetitions not to failure with total volume equalized to that in the RFG (ENFG, n = 15). The participants' sit-to-stand ability, timed-up-and-go (TUG), muscle power output in squat jump (SJ) and countermovement jump (CMJ), peak oxygen uptake (VO2peak), blood lipids and glucose, as well as blood pressure levels were assessed. A subsample of our participants (n = 22) also underwent assessment of body composition by dual X-ray absorptiometry (DXA). CT was performed twice weekly for over 12 weeks. In addition to the specific strength training (ST) programme, each group also underwent endurance training (ET) in the same session (i.e., ST immediately followed by ET). After training, all groups improved similarly and significantly in their sit-to-stand ability (P < 0.01), muscle power output relative to body mass in SJ and CMJ (P < 0.001), VO2peak (P < 0.01) and HDL cholesterol levels (P < 0.001). There were reductions in the total, leg and trunk percent fat mass as well as increases in the total, leg and trunk percent lean mass (P values ranging from P < 0.05 to P < 0.01). Independent of performing repetitions until concentric failure and greater ST volumes, all CT groups exhibited improved sit-to-stand ability, muscle power output, VO2peak and HDL cholesterol levels. In addition, our preliminary data suggest that there are no differences in the effects of the assessed CT approaches on body composition outcomes. We therefore highlight the need for additional well-powered studies to assess whether repetitions to failure could underlie distinct effects on body composition.