The research on the interactions between short and long waves or waves and currents on a variable bottom has not been made much in the past. Most of the previous analysis provided no answers to the effect on the bottom slope; thus, which can’t properly demonstrate the successive process of changes in fluid field while the short waves propagating on the long waves along gentle slope. The author’s previous studies (chen et al., 2005, 2006) on a short waves propagating over the gentle slope have gotten some reasonable results of the influence of the bottom slope. In order to describe the more practical phenomena about a progressive short waves in the nearshore zone, this study takes the advantages mentioned above and further considers the effect of tidal waves to solve the proposed topic appropriately. It mainly focuses on the understanding of the problem and establishes the mathematical model in Eulerian system to get the approached solutions. INTROCUTION RESULT Chen, Hwung and Hsu (2005): Theoretical Analysis for Surface Waves Propagation on Sloping Bottoms: Part 1, Wave Motion, vol. 42, pp Chen, Hsu, Chen and Hwung (2006): Theoretical Analysis for Surface Waves Propagation on Sloping Bottoms, Part 2: Nonlinear waves, Wave Motion, vol. 43, pp REFERENCES B.D. Yang 1 Y.Y. Chen 1,2 1 Tainan Hydraulics Lab. No. 500, Sec 3, Anming Rd, Tainan 709, Taiwan 2 National Sun Yat-sen Univ. No. 70, Lienhai Rd., Kaohsiung 80424, Taiwan PROGRESSIVE WAVES ON GENTLE SLOPE UNDER THE INFLUENCE OF TIDAL WAVES By taking tides as long waves, a definition sketch of the fluid field is given in Figure 1. It is assumed that relevant physical quantities can be expanded as a triple power series of the bottom slope, short waves steepness and long waves steepness, and the perturbation expansion system of these three parameters is illustrated as Figure 2. After systematic analysis, the asymptotic solutions up to order are obtained. METHOD The present solutions of are proposed first and have never been discussed in previous research. They demonstrate the interactions among two waves and the effect of slope. Comparing to the results of wave-wave interactions in constant depth, the present results of and include the effect of wave set-down and return flow caused by slopping bottom. The angular frequency  in short waves is modified by the above effect as where is the interacting modified quantity caused by long waves, is the same as the expression in constant depth, and is newly proposed. approches to 0 in deep water or in constant depth; otherwise, it is shown to be where denotes the wave number, the subscript 1 and 2 identify the short waves and long waves. versus the ratio of wave number under different relative depth is shown in Figure 3. Using perturbation method to solve the present subject yields great performance in this study. However, the further kinematic properities remain to be discussed in the future. Figure 2 – Illustration of the perturbation expansion system