[en] Full text: During the last decade, the geometric effect on the phase of the wave function arouse considerable interest. The conditional geometric phase is utilized to accomplish a controlled phase gate in quantum information processing. Quite recently, the concept of the geometric phase is extended to give another phase factor from a cross scalar products, thus called off-diagonal geometric phase. We investigated this off-diagonal geometric phases acquired in an evolution of a 1/2-spin system by means of a polarized neutron interferometer. Final counts with and without the polarization analysis enabled us to observe both the off-diagonal and diagonal (conventional) geometric phases in two detectors. The off-diagonal geometric phases for noncyclic evolutions were measured. Our data confirmed theoretical predictions of the off-diagonal geometric phase. The discussions on the significance of the off-diagonal geometric phase as well as the quantum eraser are presented. (author)