  Aims: The binary pulsar PSR J1811-1736 has been identified, since its
discovery, as a member of a double neutron star system. Observations of such
binary pulsars allow the measurement of general relativistic effects, which in
turn lead to information about the orbiting objects and, in a few cases, to
tests of theories of gravity. Methods: Regular timing observations have been
carried out with three of the largest European radio telescopes involved in
pulsar research. The prospects of continued observations were studied with
simulated timing data. Pulse scattering times were measured using dedicated
observations at 1.4 GHz and at 3.1 GHz, and the corresponding spectral index
has also been determined. The possibility of detecting the yet unseen companion
as a radio pulsar was also investigated. A study of the natal kick received by
the younger neutron star at birth was performed. Results: We present an up to
date and improved timing solution for the binary pulsar PSR J1811-1736. One
post-Keplerian parameter, the relativistic periastron advance, is measured and
leads to the determination of the total mass of this binary system. The pulse
profile at 1.4 GHz is heavily broadened by interstellar scattering, limiting
the timing precision achievable at this frequency and the measurability of
other post-keplerian parameters. Interstellar scattering is unlikely to be the
reason for the continued failure to detect radio pulsations from the companion
of PSR J1811-1736. The probability distribution that we derive for the
amplitude of the kick imparted on the companion neutron star at its birth
indicates that the kick has been of low amplitude.
