  In this paper, we find the radius of the disk $\Omega _{r}$ such that every
starlike logharmonic mapping $f(z)$ of order $\alpha ,$ is starlike in $%
|z|\leq r$ with respect to any point of $\Omega _{r}.$ We also establish a
relation between the set of starlike logharmonic mappings \ and the set of
starlike logharmonic mappings of order alpha. Moreover, the radius of
starlikeness and univalence for the set of close to starlike logharmonic
mappings of order $\alpha $ is determined.
