The paper presents experimental results of investigations carried out on the P91 steel and 2024 aluminium alloy under complex stress states due to various combinations of an axial force and twisting moment. An influence of out-of-phase sinusoidal and trapezoidal strain signals on the mechanical behaviour of tested materials was considered. The experiments enabled identification of the second order effects connected with the non-proportional cyclic loadings such as the phase shift between stress and strain signals during the deformation along the circular strain path, and a significant stress drop of the one of loading components applied in the case of deformation enforced by the trapezoidal signals. The experimental programme also contained the tests of monotonic tensile deformation realized simultaneously with delayed torsional cycles. They enabled to observe a drastic variations of the proportional limit and yield point of the materials in the tensile direction. This fact manifests an important material feature which can be applied to the optimal designing of some metal forming processes like an extrusion or forging for example.