Yes, React Native apps can handle complex animations with ease. React Native provides a powerful and flexible animation API that allows developers to create and control complex animations in their apps. It uses a highly performant JavaScript core combined with native UI components to deliver smooth and responsive animations. The React Native animation API supports a wide range of animations, including layout animations, transitions, and custom animations using the Animated API. With React Native, you can achieve complex animations such as parallax effects, physics-based interactions, and animated gestures. The framework also offers a variety of third-party libraries and tools that can further enhance the animation capabilities of React Native apps.