The imaginary longitudinal susceptibility &khgr;″ of polycrystalline YIG in a strong rf magnetic field with amplitudehbehaves according to the average sizex¯of the grain size distributionp(x), to its standard deviation &sgr;, and to the impurities' concentrationc. The threshold fieldh¯cincreases withcand with decreasingx¯. The slope of the tangent to &khgr;″ throughh¯cdecreases with increasingh¯cwhile, ifh¯cis constant, it increases with the impurity content. Taking into account Schlo¨mann's expression for &khgr;″ for a single crystal and a modification of Patton's transit‐time‐limited spin‐wave lifetime model, formulas for &khgr;″ andh¯cfor an impurity‐doped polycrystalline aggregate of spheres having lognormally distributed diameters are worked out. A graphical method to infer the relevant parameters from the experiment is presented. Experimental data and theory are compared on two pairs of compositions; the first one exhibiting a moderateh¯c(∼ 15 Oe) and a second one, a highh¯c([inverted lazy s] 40 Oe). Each pair consists of a fine‐grained YIG and an impurity‐doped YIG. The agreement is qualitatively satisfactory. The modifications resulting from Scotter's inclusion/porosity scattering model are also briefly treated.