  A theoretical analysis of possible influence of neutrino magnetic moments on
the propagation of ultrahigh-energy cosmic neutrinos in the interstellar space
is carried out under the assumption of two-neutrino mixing. The exact solution
of the effective equation for neutrino evolution in the presence of a magnetic
field and matter is obtained, which accounts for four neutrino species
corresponding to two different flavor states with positive and negative
helicities. Using most stringent astrophysical bounds on the putative neutrino
magnetic moment, probabilities of neutrino flavor and spin oscillations are
calculated on the basis of the obtained exact solution. Specific patterns of
spin-flavor oscillations are determined for neutrino-energy values
characteristic of, respectively, the cosmogenic neutrinos, the
Greisen-Zatsepin-Kuz'min (GZK) cutoff, and well above the cutoff.
