For elastic curvilinear rods, a matrix equation of dynamic stability is derived. An external load that lies in the plane to which the axis of the curvilinear rod belongs rotates, making the initial angle with the curved axis of the rod. The obtained coefficients of the matrix equation are different from those known in the literature. As a special case of integro-differential equations of dynamic stability, an integral equation of static stability of curvilinear rods is obtained, which is known in the literature.