In the GASSCF method orbitals are variationally optimized via a self-consistent field (SCF) procedure, under the mean field generated by the GAS wave function. As in CASSCF, all intraspace orbital rotations, such as GAS1 ↔ GAS1 or GAS2 ↔ GAS2, are redundant and already described by the intra-space excitations in the CI-expansion; thus, these excitations are excluded from the orbital optimization. Interspace orbital rotations such as GAS1 ↔ GAS2, however, are only partially redundant and have to be considered in the GASSCF orbital optimization step, in addition to inactive-active, inactive-virtual, and active-virtual rotations. As some of these rotations are already represented by the GAS wave functions, linear dependencies are introduced, that often have a negative impact on the rate of convergence of the GASSCF procedure. Also of interest is the structure of the 1-RDM for GAS wave functions. For disconnected GAS spaces the 1-RDM is block diagonal, because off-diagonal elements, which couple orbitals belonging to different GAS subspaces, vanish. Thus, the diagonalization of the 1-RDM for disconnected GAS, which lead to the natural orbitals, represents an invariant orbital transformation. For connected GAS subspaces, the off-diagonal elements between orbitals belonging to different GAS spaces in general do not vanish, and diagonalization of the onebody density matrix becomes a non-invariant rotation, that mixes orbitals from different GAS subspaces. Thus, natural orbital occupation numbers are only well defined for disconnected GAS spaces. For connected spaces we can define "pseudo-natural orbitals" which are obtained from the block diagonalization of the 1-RDM, each block referring to orbitals of one GAS subspace. Pseudo-natural orbitals and natural orbitals are identical for disconnected spaces.