The article presents the results of experimental research and numerical simulation of the amplitude-frequency characteristics (AFC) of the voltage transmission ratio (voltage gain) |Ku| and frequency characteristics of the voltage standing wave ratio from the input (input VSWR) to three bandpass filters on the waveguide-slot membranes (WSM) with L-shaped resonance slot: to the single stage, to the three stages and to the four stages. The filter designs are given in article. The results of numerical simulation and experimental study show that in the frequency range 5,0...8,5 GHz filters provide attenuation behind the pass band up to 30 dB at the level of the introduced losses in the pass-band from 0,2 to 1,0 dB. The values of the calculated and experimental input VSWR in the filter bandwidth of pass-band are from 1,1 to 1,74 relative units (r. u.) and in the stop bands from 2 to 300 r. u. The authors believe that using of waveguide-slot membranes will significantly reduce the overall dimensions of microwave bandpass and bandstop filters in the middle of the centimeter wavelength range.