Present experimental data do not exclude fast oscillation of the neutron n to its degenerate twin from a hypothetical parallel sector, the so called mirror neutron n . We show that this effect brings about remarkable modifications of the ultrahigh-energy cosmic ray spectrum testable by the present Pierre Auger Observatory (PAO) and Telescope Array (TA) detector, and the future JEM-EUSO experiment. In particular, the baryon non-conservation during UHECR propagation at large cosmological distances shifts the beginning of the GZK cutoff to lower energies, while in the presence of mirror sources it may enhance the spectrum at E > 100 EeV. As a consequence, one can expect a significant reduction of the diffuse cosmogenic neutrino flux.There may exist a hidden parallel sector that is an exact copy of our particle sector. One can imagine a theory based on a direct product G × G of identical gauge factors with identical particle contents which can emerge, e.g. in the context of E 8 × E 8 string theory. As a minimal possibility, one can consider a case of two Standard Model copies with G = SU (3) × SU (2) × U(1) standing for ordinary sector and G = SU (3) × SU (2) × U(1) standing for parallel sector. Alternatively, one can envisage some grand unified extensions as SU (5) × SU (5) , etc. The Lagrangians of two worlds can be rendered identical to each other, with all coupling constants being exactly the same in both sectors, by introducing a discrete symmetry G ↔ G under the exchange of two gauge systems and of the respective matter fields.A well-known example, coined as mirror world [1-6], was introduced a long time ago for interpreting parity as a discrete symmetry when our 'left-handed' particles are exchanged with their mirror twins that are 'right-handed'. a e-mail: zurab.berezhiani@aquila.infn.it b e-mail: askhat.gazizov@desy.de Concerns about parity are irrelevant for our following discussions, which can be extended to a parallel sector (or sectors) of any chirality. For us is important only that each ordinary particle: electron e, proton p, neutron n etc. may have a mass degenerate twin: e , p , n etc. These twin particles must be sterile to our strong and electroweak interactions but have their own strong and electroweak interactions among themselves. 1 Mirror baryons can be viable as asymmetric dark matter provided that parallel sector has smaller temperature than the ordinary one, T T [7][8][9][10]. On the other hand, once this condition is fulfilled, B-L and CP violating interactions among ordinary and mirror particles can generate baryon asymmetries in both sectors [11,12], naturally giving the relation Ω B /Ω B 5 between cosmological fractions of the dark and visible matter [13][14][15]. Such interactions can be mediated by heavy messengers coupled to both sectors, as right handed neutrinos or extra gauge bosons/gauginos [16]. In the context of extra dimensions, ordinary and mirror sectors can be modeled as two parallel 3-dimensional branes and particle processes between them could be mediated by the...