In this paper the extended KdV equation \[ \eta_t+ 6\eta\eta_x+ \eta_{xxx}+ \alpha c_1\eta^2\eta_x+\alpha c_2\eta_x\eta_{xx}+\alpha c_3\eta\eta_{xxx}+\alpha c_4\eta_{xxxxx}=0 \quad (\alpha\leq1)\tag{1} \] and the modified KdV equation \(\eta_t+6\eta^2\eta_x+\eta_{xxx}=0\) are studied. From (1) the following extended KdV equation can be deduced \[ u_t+6uu_\xi+ u_{\xi\xi\xi}+ \alpha'u^2u_\xi+ {\textstyle{2\over3}} \alpha'u_\xi u_{\xi\xi}+ {\textstyle{1\over3}} \alpha'uu_{\xi\xi\xi}+ {\textstyle{1\over30}} \alpha'u_{\xi\xi\xi\xi\xi}=0 \tag{2} \] by using the transformation \[ \eta=u+ \alpha\Bigl( {\textstyle{{{3c_2}\over2}- {c_1\over6}}}- 10c_4\Bigr)u^2+\alpha \Bigl( {\textstyle{{c_2\over12}+ {2c_3\over3}- {c_1\over12}-{{35c_4}\over6}}} \Bigr)u_{xx}, \]
\[ \tau=t+\alpha \Bigl({\textstyle{{{5c_4}\over3}- {c_3\over6}}} \Bigr)x, \qquad \xi=x, \quad \alpha\leq 1. \] The authors obtain the two-soliton solution of (2): \[ {1\over8}u= {{(k^*_1)^2f_1+ (k^*_2)^2f_2+ (k^*_2-k^*_1)f_1f_2+ m[(k^*_2)^2f^2_1f_2+ (k^*_1)^2f_1f^2_2]} \over {(1+f_1+f_2+ mf_1f_2)^2}}, \] where \(f_1=\exp 2k^*_i(V^*_i\tau- \xi+s_i)\) \((i=1,2)\), \(V^*_i=2A^*_i+ \alpha'{2\over15} (A^*_i)^2\) and \(m=({{k^*_2-k^*_1} \over {k^*_2+k^*_1}})^2\).