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This paper studies the random inteal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom.The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins (1963) and Dean (1979) in the study of random surface waves and by Song (2004) in the study of secondorder random wave solutions for inteal waves in a two-layer fluid.The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes,wave numbers and frequencies,and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other.They also show that the second-order solutions consist of two parts:the first one is the first-order solutions,and the second one is the solutions of the second-order asymptotic equations,which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces.Both the first-order and second-order solutions depend on the density and depth of each layer.It is also deduced that the results of the present work include those derived by Song (2004) for second-order random wave solutions for inteal waves in a two-layer fluid as a particular case.