Electronic Journal of Differential Equations, Vol. 2014 (2014), No. 16, pp. 1-11. Title: Meromorphic solutions to complex difference and q-difference equations of Malmquist type Authors: Jie Zhang (China Univ. of Mining and Technology, Xuzhou, China) Jianjun Zhang (Jiangsu Second Normal Univ., Nanjing 210013, China) Abstract: In this article, we study the zeros, poles and fixed points of finite order transcendental meromorphic solutions of complex difference and q-difference equations of Malmquist type respectively. Some examples are structured to show that our results are sharp. Submitted September 13, 2013. Published January 10, 2014. Math Subject Classifications: 30D35, 34M10. Key Words: Meromorphic; differential-difference equation; fixed point; order.