This paper focuses on the development of a wind gust load alleviation control system for implementation in very flexible aircraft. The gust load alleviation system is designed using Linear Quadratic Gaussian (LQG) control techniques, and it is based on a nonlinear model of the coupled rigid-body and elastic modes of a very flexible aircraft. The nonlinear model contains the dynamics of the aircraft body reference frame, elastic strains, strain rates and unsteady aerodynamic flow states. The nonlinear model is linearized at a typical operating point corresponding to steady straight level flight conditions. Using model order reduction techniques, a lower order control-oriented model for the longitudinal dynamics of the very flexible aircraft is obtained. Assuming that the gust field is stochastic, the aircraft model is augmented with the disturbance model that matches the experimentally observed von Karman and Dryden power spectral density characteristics. A LQG controller is then designed to reduce the structural deflections, as the aircraft responds to the gust. Additionally, a command tracking control system is presented for longitudinal flight, which tracks a pitch angle command in the presence of a gust disturbance. It is demonstrated that the hard limits on the structural deflections while responding to the pitch angle command can be enforced using reference governor techniques.