  We study the dynamics induced by an $m$-linear operator. We answer a question
of B\`es and Conejero showing an example of an $m$-linear hypercyclic operator
acting on a Banach space. Moreover we prove the existence of $m$-linear
hypercyclic operators on arbitrary infinite dimensional separable Banach
spaces. We also prove an existence result about symmetric bihypercyclic
bilinear operators, answering a question by Grosse-Erdman and Kim.
