Abstract
This paper has two parts. In part Ⅰ, existence and uniqueness theorem is established for solutions of neutral stochastic differential equations with variable delays driven by \begin{document}$ G $\end{document} -Brownian motion (VNSDDEGs in short) under global Caratheodory conditions. In part Ⅱ, a simplified VNSDDEGs for the original one is proposed. And the convergence both in \begin{document}$ L^p $\end{document} -sense and capacity between the solutions of the simplified and original VNSDDEGs are established in view of the approximation theorems. Two examples are conducted to justify the theoretical results of the approximation theorems.
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