Let (X,d) be a compact metric space and (K(X),dH) be the space of all non-empty compact subsets of X equipped with the Hausdorff metric dH. The dynamical system (X,f) induces another dynamical system (K(X),f{topbar}). We study the relations between the various forms of sensitivity of the systems (X,f) and (K(X),f{topbar}). We prove that all forms of sensitivity of (K(X),f{topbar}) partly imply the same for (X,f), and the converse holds in some cases. © 2010 Elsevier B.V.