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The neutrinoless double beta decay (0νββ-decay) transition to the first excited 0 + collective final state is examined for A=76, 82, 100 and 136 nuclei by assuming light and heavy Majorana neutrino exchange mechanisms as well as the trilinear R-parity violating contributions. Realistic calculations of nuclear matrix elements have been performed within the renormalized Quasiparticle Random Phase Approximation. Transitions to the first excited twoquadrupole phonon 0 + state are described within a boson expansion formalism and alternatively by using the operator recoupling method. We present the sensitivity parameters to different lepton number violating signals, which can be used in planning the 0νββ-decay experiments. The half-life of 0νββ-decay to the first excited state 0 + 1 is by a factor of 10 to 100 larger than that of the transition to the ground state, 0 + g.s. .