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We consider the class of higher derivative field equations whose waveoperator is a square of another self-adjoint operator of lower order. At thefree level, the models of this class are shown to admit a two-parameter seriesof integrals of motion. The series includes the canonical energy. Everyconserved quantity is unbounded in this series. The interactions are includedinto the equations of motion such that a selected representative in conservedquantity series is preserved at the non-linear level. The interactions are notnecessarily Lagrangian, but they admit Hamiltonian form of dynamics. The theoryis stable if the integral of motion is bounded from below due to theinteraction. The motions are finite in the vicinity of the conserved quantityminimum. The equations of motion for fluctuations have the derived form with noresonance. The general constructions are exemplified by the models of thePais-Uhlenbeck oscillator with multiple frequency and Podolsky electrodynamics.The example is also considered of stable non-abelian Yang-Mills theory withhigher derivatives.

Resonance and stability of higher derivative theories of derived type