Natural hazards and excitations often exhibit stochastic characteristics, such as winds, earthquakes, and ocean waves. These load scenarios deserve extensive attention and investigation that account for the uncertain characteristics; otherwise, it may lead to unpredictable damage. In addition, the viscoelasticity phenomenon is prevalent in a variety of engineering materials. When resisted by dynamic loads, the viscoelastic materials exhibit viscous, smoothly varying, and time-dependent deformation, associated with energy dissipation. It can be essential to understand the viscoelastic behavior and its potential influence on structural response, particularly when structural design and response analysis are considered. In this regard, during recent decades it has been shown that the implementation of fractional derivatives allows a more descent description of the viscoelasticity phenomenon. Therefore, in this thesis, the challenge of viscoelastic oscillators subjected to evolutionary stochastic loads is addressed. More specifically, the fractional-order derivative element is introduced to effectively represent the viscoelastic nature of the materials. Further, several analytical and numerical methods are examined. To start, the statistical linearization method is extended for oscillators with fractional derivative elements, where a quite versatile discretization approach is introduced that makes the proposed method applicable to any kind of nonlinearity. Next, the stochastic averaging method is applied on fractional oscillators reducing the dimensionality of the system, and thus accelerates the following computation. Thirdly, the wavelets-galerkin method is adopted to address the evolutionary response statistics of either linear or nonlinear systems. Note that, by accounting unnoticeable overlapping of the basis wavelets functions, the method predicts accurately responses of relatively flexible and/or lightly damped systems. Results in juxtaposition with the pertinent Monte Carlo simulation data demonstrate the reliability and accuracy of the proposed methods of analysis.