By convention, the marked dominance in the peak region of a state with well-defined quantum numbers such as angular momentum, parity, isotopic spin, and hypercharge is called a particle. As a function of energy, the influence of such a state is centered on the peak with a characteristic haIf-width. The occurrence in meson systems of peaks which, even though sharp, cannot be called particles in the conventional sense is discussed. The effect does not occur in only one angular momentum state. It may, in general, occur at the same energy in more than one isotopic spin state. Finally, the peak has a characteristic asymmetric distribution which cannot be described by a Breit-Wigner formula. Moreover, if the peak occurs in a 3-particle state, there is a characteristic Dalitz-Fabri plot (Phil. Mag. 44, 1068(l953); Nuovo Cimento ll, 479(l954)) associated with it. (L.N.N.)