<p>Fractional quantum Hall effect states have been studied on samples with an electron system formed by two layers of two-dimensional electrons of different densities in a wide (60 nm) GaAs quantum well. The experiment has been carried out at a temperature of 45 mK in an inclined magnetic field, where these states are more pronounced. It has been established that insignificant changes in the relation between electron densities by means of gate voltages can significantly change the picture of the observed states At various combinations of electron densities in the layers, pronounced quantized plateaus in the Hall resistance <i>R</i>_<i>xy</i> = <i>q</i>(<i>h</i>/<i>e</i>²) with quantum numbers <i>q</i> = 4/5, 3/4, 3/8, and 3/7 have been detected. Using the magnetocapacitive method, it has been established that the states with <i>q</i> = 4/5 and 3/4 or <i>q</i> = 3/8 and 3/7 arise when an incompressible state in a layer with a higher electron density exists due to a jump in the chemical potential of the layer between different spin Landau sublevels, which occurs when one or two sublevels are filled with the layer electrons, respectively. It has been established that the variation of the magnetic field makes it possible to implement two states of the fractional quantum Hall effect with <i>q</i> = 3/8 and 3/7 in the same incompressible state in the higher-density layer, which is broadened in the field due to the transition of electrons between layers, which occurs under the variation of the field.</p>