We consider the scalar nonautonomous neutral delay differential equation with variable delays \[ \frac d{dt}\bigg[x(t)+um^{\ell}_{j=1}p_j(t)x(t)-au_j(t))\bigg]+um^{m}_{i=1}q_i(t)x(t-igma_i(t))=0 \] for $t_0\leq t<T\leq\infty$. Using the method of characteristic equations, we give conditions for the existence of positive solutions. Our theorems generalize and extend the results for simpler cases proved by Chuanxi, Ladas [1] and Gyori, Ladas [5].