Explicit and implicit time integration techniques are frequently required in numerical approaches. Explicit schemes are constrained by stringent stability requirements, yet they are straightforward and affordable per time step. Conversely, implicit techniques allow for considerably bigger time steps but also increase computational costs by requiring the solution of complex systems at each iteration. Thus, objective of developing more efficient time integrators methods for stiff systems is to provide alternative methods which have better stability properties than explicit schemes and require fewer arithmetic operations per time step than implicit methods. We present recent work on exponential time differencing (ETD) methods. ETD methods efficiently handle stiffness by treating linear and nonlinear terms separately, allowing larger time steps without losing accuracy. Inspired by Cox and Matthews's work, we are developing a two-stage exponential time differencing (ETD) technique that preserve key physical properties, such as energy dissipation and stability. Numerical experiments demonstrate that the proposed methods achieve high accuracy and robustness, even for long-time simulations. This work contributes to the development of structure-preserving and computationally efficient techniques for nonlinear partial differential equations.