Summary: In this paper, we introduced the idea of relative Nevanlinna \(L^\ast\)-order and relative Nevanlinna \(L^\ast\)-lower order of an analytic function of several complex variables with respect to an entire function of several complex variables in the unit polydisc. Also we study some growth properties of composition of two analytic functions of several complex variables in the unit polydisc on the basis of their relative Nevanlinna \(L^\ast\)-order and relative Nevanlinna \(L^\ast\)-lower order.