The nonlinear interactions between tidal waves propagating in an infinite shallow canal with constant width and depth are analysed. The friction is assumed to be proportional to the square of velocity and regarded as partially nonlinear. A comparison between the magnitude of nonlinearity of fric-tional origin with that of nonfrictional origin is given. The exact expressions of the coefficients of the Fourier expansion of |u|u are obtained when u contains two waves, and an approximate expansion is also obtained when u contains three or more waves. Approximate solutions for primary and subordinate waves are given, showing (i) when the primary waves travel together, the smaller wave will decay at a faster rate; (ii) subordinate waves experience the processes of growth and decay owing to friction; (iii) because of frictional nonlinearity, the practical ranges of variation of the nodal factors f used in tidal analysis and prediction should usually be smaller than the theoretical ones, (iv) the growth of over The nonlinear interactions between tidal waves propagating in an infinite shallow canal with constant width and depth are analyzed. The friction is assumed to be proportional to the square of velocity and as as partially nonlinear. A comparison between the magnitude of nonlinearity of fric-tional origin with that of nonfrictional origin is given. The exact expressions of the coefficients of the Fourier expansion of | u | u are obtained when u contains two waves, and an approximate expansion is also obtained when u contains three or more waves. Approximate solutions for primary and subordinate waves are given, showing (i) when the primary waves travel together, the smaller wave will decay at a faster rate; (ii) subordinate waves experience the processes of growth and decay due to friction; (iii) because of frictional nonlinearity , the practical variation of the nodal factors f used in tidal analysis and prediction should usually be smaller than the theoretical ones, (iv) the growth of over