Well-resolved large-eddy simulations are used to study adverse-pressure-gradient (APG) turbulent boundary layers (TBLs) under near-equilibrium conditions. In particular, we focus on two near-equilibrium cases where the power-law freestream velocity distribution is adjusted in order to produce long regions with a constant value of the Clauser pressure-gradient parameter β. In the first case we obtain an APG TBL with a constant value of β ≃ 1 over 37 average boundary-layer thicknesses, and in the second one a constant value of β ≃ 2 for around 28 average boundary-layer thicknesses. The scaling law suggested by Kitsios et al. (Int J Heat Fluid Flow 61:117–128, 2016, [10]), proposing the edge velocity and the displacement thickness as scaling parameters, was tested on the two constant-pressure-gradient parameter cases. The mean velocity and Reynolds-stress profiles were found to be dependent on the downstream development, a conclusion in agreement with classical theory.