In this paper we present the asynchronous implementation of Halley-like method for the simultaneous approximation of polynomial roots on a distributed memory multicomputer. It is shown that the lower bound of the order of convergence of asynchronous Halley-like, method with the delay $r$ is at least $\eta A>3$, where $\eta A$ is the unique positive root of the equation $\eta^{r+1}-3\eta^r-1=0$. The computational efficiency of the synchronous and asynchronous versions are studied in the case of hypercube topology.