This paper presents a general framework for constructing higher-order, unconditionally energy-stable exponential time differencing Runge–Kutta (ETDRK) methods for gradient flows. The authors identify conditions that must be satisfied for ETDRK schemes to maintain energy stability. They show that widely used third- and fourth-order ETDRK schemes do not meet these conditions. To address this, they introduce new third-order ETDRK schemes with appropriate stabilization, which satisfy the conditions and guarantee unconditional energy decay. The authors conduct extensive numerical experiments to verify the accuracy, stability, behavior under large time steps, long-term evolution, and adaptive time stepping strategy across various gradient flows. This study is the first to examine the unconditional energy stability of high-order ETDRK methods. The authors are optimistic that their framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable. The paper also discusses the energy stability of ETDRK schemes for different gradient flows, including the Allen–Cahn, Cahn–Hilliard, and phase-field crystal models. The authors show that the new third-order ETDRK schemes are unconditionally energy stable and perform well in numerical experiments with different time steps and stabilization constants. They also present an adaptive time-stepping strategy that takes advantage of the unconditional energy stability of the schemes. The results demonstrate that the new ETDRK schemes are accurate and stable for a wide range of gradient flows.This paper presents a general framework for constructing higher-order, unconditionally energy-stable exponential time differencing Runge–Kutta (ETDRK) methods for gradient flows. The authors identify conditions that must be satisfied for ETDRK schemes to maintain energy stability. They show that widely used third- and fourth-order ETDRK schemes do not meet these conditions. To address this, they introduce new third-order ETDRK schemes with appropriate stabilization, which satisfy the conditions and guarantee unconditional energy decay. The authors conduct extensive numerical experiments to verify the accuracy, stability, behavior under large time steps, long-term evolution, and adaptive time stepping strategy across various gradient flows. This study is the first to examine the unconditional energy stability of high-order ETDRK methods. The authors are optimistic that their framework will enable the development of ETDRK schemes beyond the third order that are unconditionally energy stable. The paper also discusses the energy stability of ETDRK schemes for different gradient flows, including the Allen–Cahn, Cahn–Hilliard, and phase-field crystal models. The authors show that the new third-order ETDRK schemes are unconditionally energy stable and perform well in numerical experiments with different time steps and stabilization constants. They also present an adaptive time-stepping strategy that takes advantage of the unconditional energy stability of the schemes. The results demonstrate that the new ETDRK schemes are accurate and stable for a wide range of gradient flows.