Summary: A new set of integral quadratic constraints (IQC) is derived for a class of rate limiters, modelled as a series connections of saturation-like memoryless nonlinearities followed by integrators. The result, when used within the standard IQC framework (in particular, with finite gain/passivity-based arguments, Lyapunov theory, structured singular values, etc.), is expected to be widely useful in nonlinear system analysis. For example, it enables discrimination between saturation-like and deadzone-like nonlinearities and can be used to prove stability of systems with saturation in cases when replacing the saturation block by another memoryless nonlinearity with equivalent slope restrictions makes the whole system unstable. In particular, it is shown that the \(L_2\) gain of a unity feedback system with a rate limiter in the forward loop is bounded. In addition, a new, more flexible version of the general IQC analysis framework is presented, which relaxes the homotopy and boundedness conditions, and is more aligned with the language of the emerging IQC software.