A quasi-static transmission-line method, as used in antenna theory, and modified to take into account effects of radiation damping, is applied to the problem of waveguide coupling through slots which may be large enough to exhibit resonance effects. It is shown that the waveguide environment significantly alters the value to be used for the slot characteristic impedance, although this quantity cannot itself be calculated by the present analysis. The method is applied in detail to the case of axially-coupled waveguides and to guides coupled, via a common broad wall, through crossed slots. It is shown that a narrow slot needs to be very near resonance to give a coupling as large as that from a circular hole of comparable dimensions.