Nonlinearity is ubiquitous. Further, nonlinear systems comprising elements with fractional order differentiation operators have received increasing attention in recent decades. Furthermore, systems exposed to stochastic excitations are quite common in engineering practice. The lecture will address issues relating to the determination of the response of stochastically excited nonlinear systems involving fractional order differentiation. In this regard, the technique of statistical linearization in various formats and versions will be discussed. This will be done in conjunction with an examination of the applicability of the related concepts of stochastic averaging, and harmonic balance In the process, the computational complexity and tediousness of determining the exact non-stationary stochastic response even of linear systems will be pointed out. Comments regarding cases involving combinations of stochastic and periodic excitations will be made. The analytical/semi-analytical results will be juxtaposed with data from pertinent Monte Carlo simulations. Some possible extensions or variations of the discussed approaches will also be outlined.