Pseudorandom test techniques are widely used for measuring the impulse response (IR) for linear devices and Volterra kernels for nonlinear devices, especially in the acoustics domain. This paper studies the application of pseudorandom functional test techniques to linear and nonlinear MEMS Built-In-Self-Test (BIST). We will first present the classical pseudorandom BIST technique for Linear Time Invariant (LTI) systems which is based on the evaluation of the IR of the Device Under Test (DUT) stimulated by a Maximal Length Sequence (MLS). Then we will introduce a new type of pseudorandom stimuli called the Inverse-Repeat Sequence (IRS) that proves better immunity to noise and distortion than MLS. Next, we will illustrate the application of these techniques for weakly nonlinear, purely nonlinear and strongly nonlinear devices.