We demonstrate a crucial role of fractional occupation numbers (FONs) of natural orbitals (NOs) in the description of double excitations in time-dependent NO functional theory (TDNOFT). An analytical dependence of the double excitation energy omega(alpha) on the ratio of the FONs is derived in a model from the matrix diagonalization problem. In the large ratio Heitler-London limit the derived formula reproduces the correct asymptotics of omega(alpha) of the ionic state of double excitation character. In the small ratio Moller-Plesset, MP limit the reverse relation of static MP perturbation theory emerges in the dynamical response theory to provide omega(alpha). (C) 2017 Elsevier B.V. All rights reserved.