An exact method is presented for the design of band-stop filters consisting of stubs and quarter-wavelength connecting lines. Using this method a low-pass prototype circuit is chosen, AND THE TRANSMISSION-LINE BAND-STOP FILTER DERIVED FROM THE PROTOTYPE WILL HAVE A RESPONSE THAT IS AN EXACT MAPPING OF THE PROTYPE RESPONSE. In theory the stop band can have any width, but if the stop band is very narrow the stub impedances become unreasonable. In such cases it is found to be desirable to replace the stubs by capacitively or inductively coupled resonators of reasonable impedance. This introduces an approximation but gives very good results. The design of filters having three-quarter-wavelength spacings between resonators is also discussed. This latter case is of interest for the design of waveguide band-stop filters where it has been found to be desirable to separate the resonators by three quarter-wavelengths in order to avoid interactions between the fringing fields at the coupling irises.