An investigation is made of the relation between scattering lengths and resonances in a two-nucleon system. For resonances Eo near zero energy the usual determination of an effective optical potential in mesonic atoms is limited, and it is shown here that the scattering length can only be represented usefully as a sum over resonances of the compound system if the condition IEolDI ~ (PDo)! Is satisfied, where D is the average spacing of s-wave states, p the density of target nucleons and Do the Compton volume of the reduced system. This condition is seen to be valid for mr:, nK and KK interactions and these systems are considered in some detail. It is shown that knowledge of the level shifts of each of these examples can help resolve present uncertainties in associated boson structure.