  Semileptonic decays of the $\Xi_b$ baryon are studied in the framework of the
relativistic quark-diquark model based on the quasipotential approach. The weak
decay form factors are calculated with the comprehensive account of all
relativistic effects without employing nonrelativistic and heavy quark
expansions. On this basis differential and total decay rates as well as
different asymmetry parameters are calculated for the heavy-to-heavy $\Xi_b\to
\Xi_c\ell\nu_\ell$ and heavy-to-light $\Xi_b\to \Lambda\ell\nu_\ell$
semileptonic decays. Predictions for the ratios of such decays involving $\tau$
lepton and muon are presented.
