  The behaviour of the topological susceptibility \chi in QCD with two colours
and 8 flavours of quarks is studied at nonzero temperature on the lattice
across the finite density transition. It is shown that the signal of \chi drops
abruptly at a critical chemical potential \mu_c, much as it happens at the
finite temperature and zero density transition. The Polyakov loop and the
chiral condensate undergo their transitions at the same critical value \mu_c.
At a value \mu_s of the chemical potential, called saturation point, which in
our case satisfies \mu_s > \mu_c, Pauli blocking supervenes and consequently
the theory becomes quenched.
