  We investigate several possibilities of obtaining a {\L}ojasiewicz inequality
for definable multifunctions and give some examples of applications thereof. In
particular, we prove that the Hausdorff distance and its extension to closed
sets is definable when composed with definable multifunctions. This allows us
to obtain {\L}ojasiewicz-type inequalities for definable multifunctions
obtained from Clarke's subgradient or the tangent cone. The paper ends with a
{\L}ojasiewicz-type subgradient inequality in the spirit of
Bolte-Daniilidis-Lewis-Shiota or Ph\d{a}m.
