1. At a computer system including at least one processor and a memory, in a computer networking environment including a plurality of computing systems, a computer-implemented method for rendering animations in a multi-layered animation system, the method comprising: establishing a first value which is an operating system (OS)-specified animation value for at least one property of a user interface (UI) element that is to be animated; receiving a second value which is a user-specified animation value for the at least one property of the UI element that is to be animated; determining a manner of combining, based at least in part on the UI element property and at least in part on the type of animation value, which specifies how to combine the first OS-specified animation value and the second user-specified animation value; calculating a third value in the determined manner by combining the first OS-specified animation value and the second user-specified animation value for the UI element, wherein the third value is a combination of the first and second values calculated according to the determined manner of combining; sending the calculated third value to an animation rendering module for rendering the UI element; and rendering the animation for the element using the third value of the combined animation values.