Within the framework of linear quantum field theories, a general study is presented of the existence and removal of runaway modes—solutions of the equations of motion which exhibit a real exponential time dependence. It is hoped that this work will yield insight into the corresponding problem in physically realistic theories. It is shown that runaway modes occur only when the Hamiltonian is not positive definite, and that they occur in linear quantum theories whenever they appear in the corresponding classical theories. Three methods are proposed for eliminating these unphysical modes One is the analog of the method used by Dirac in classical electron theory; the other two are believed to be new.