Bi-layered cylinders under torsion, axial and combined loadings are investigated on the basis of second-order elasticity. Besides the Poynting effect, in which a cylinder elongates or contracts axially under torsion, a coupled axial force-twist effect is found under combined loading. In this latter phenomenon, the twist of a torsionally loaded cylinder is affected by the axial loading. Numerical results indicate that both these nonlinear phenomena cannot be ignored for soft materials. Explicit parameters for judging the sign of the effects, i.e., whether the axial loading causes the cylinder to increase or reduce the twist in the case of the axial force-twist effect, and whether it elongates or shortens in the case of the Poynting effect, are studied. It is found that these effects in a soft composite may be significantly amplified over those in homogeneous materials and that they are strongly influenced by the material parameters and by the interface position. Comparison of the theoretical results with the torque-tension-twist data for cardiac papillary muscles shows reasonable agreement. The solutions also provide the basis for a mechanistic method for determining third-order elastic constants.