  PSR J1906+0746 is a young pulsar in the relativistic binary with the
second-shortest known orbital period, of 3.98 hours. We here present a timing
study based on five years of observations, conducted with the 5 largest radio
telescopes in the world, aimed at determining the companion nature. Through the
measurement of three post-Keplerian orbital parameters we find the pulsar mass
to be 1.291(11) M_sol, and the companion mass 1.322(11) M_sol respectively.
These masses fit well in the observed collection of double neutron stars, but
are also compatible with other white dwarfs around young pulsars such as
J1906+0746. Neither radio pulsations nor dispersion-inducing outflows that
could have further established the companion nature were detected. We derive an
HI-absorption distance, which indicates that an optical confirmation of a white
dwarf companion is very challenging. The pulsar is fading fast due to geodetic
precession, limiting future timing improvements. We conclude that young pulsar
J1906+0746 is likely part of a double neutron star, or is otherwise orbited by
an older white dwarf, in an exotic system formed through two stages of mass
transfer.
