Simplified finite element methods for finite deformation, post-buckling analysis of large space trusses and space frames are presented. Arbitrarily large rigid translations and rigid rotations of each member are accounted for. Each 3-D truss member is assumed to withstand an axial force, while each 3-D frame member is assumed to withstand two bending moments, a twisting moment, and transverse and axial forces at each node. The influence of local (member) buckling on global instability is systematically examined. For both 3-D truss and frame members, explicit tangent stiffness matrices are derived. By 'explicit;' it is meant that no element-wise basis functions are assumed and that no element-wise numerical integrations are involved. These explicit tangent stiffness matrices are very simply evaluated at any point in the load deformation history of a space truss, or space frame, undergoing large deformations, as well as in the post-buckled region of behavior of these structures. An arc-length method is implemented to trace the post-buckling behavior of these large space structures. A large number of examples are included to: (1) bring out the economy as well as accuracy of the simplified method developed; (2) indicate the effectiveness of the present method in creating reduced-order models of large space structures; and (3) delineate the process whereby the overall behavior of the structure can be vastly improved by controlling the deformation of individual members through active or passive mechanisms. Keywords: Reduced order model; Simplified nonlinear analysis; Finite deformations; Finite rotations; Semi-tangential rotations; Exact tangent stiffness matrix; LSS (Large Space Structure) control; Arc-length method.