Let $\Sigma_p$ denote the class of functions of the form $f(z)=z^p+\Sigma^\infty_{n=p}a_nz^n$ $(p\in N)$. Two new subclasses $H_{p,k}(\lambda,A,B)$ and $Q_{p,k}(\lambda,A,B)$ of meromorphically multivalent functions starlike with respect to $k$-symmetric points in $\Sigma_p$ are investigated. Certain convolution properties for these subclasses are obtained.