Properties of growing waves are investigated in a uniform plasma with a doubly humped velocity distribution by studying the character of the boundary curves between growing waves and damped waves. The specific family of distribution functions mainly investigated is one which is composed of a Maxwellian main part plus a small gentle bump (also Maxwellian) on its tail. When a parameter describing the shape of the distribution (the relative strength of the small bump, the separation between the two peaks, etc.) is changed from the region of stability, there is a certain wavenumberkcat which the onset of plasma‐wave instabilities is expected. Studies are made of the conditions for whichkcvanishes, sincekc= 0 is associated with a special kind of excitations. A proof is given that the growing wave is not on the same branch of the solution to the dispersion relation as the usual plasma wave.