  A celebrated result of Hal\'asz describes the asymptotic behavior of the
arithmetic mean of an arbitrary multiplicative function with values on the unit
disc. We extend this result to multilinear averages of multiplicative functions
providing similar asymptotics, thus verifying a two dimensional variant of a
conjecture of Elliott. As a consequence, we get several convergence results for
such multilinear expressions, one of which generalizes a well known convergence
result of Wirsing. The key ingredients are a recent structural result for
bounded multiplicative functions proved by the authors and the mean value
theorem of Hal\'asz.
