In this paper, the well-posedness of the higher-order Benjamin–Ono equation u t + ℋ (u x x) + u x x x = u u x - ∂ x (u ℋ ∂ x u + ℋ (u ∂ x u) ) u_{t}+\mathcal{H}(u_{xx})+u_{xxx}=uu_{x}-\partial_{x}(u\mathcal{H}\partial_{x}% u+\mathcal{H}(u\partial_{x}u)) is considered. The modified energy method is introduced to consider the equation. It is shown that the Cauchy problem of the higher-order Benjamin–Ono equation is locally well-posed in H 3 / 4 {H^{3/4}} without using the gauge transformation. Moreover, the well-posedness of the higher-order intermediate long wave equation u t + 𝒢 δ (u x x) + u x x x = u u x - ∂ x (u 𝒢 δ ∂ x u + 𝒢 δ (u ∂ x u) ) , 𝒢 δ = ℱ x - 1 i (coth (δ ξ)) ℱ x , u_{t}+\mathcal{G}_{\delta}(u_{xx})+u_{xxx}=uu_{x}-\partial_{x}(u\mathcal{G}_{% \delta}\partial_{x}u+\mathcal{G}_{\delta}(u\partial_{x}u)),\quad\mathcal{G}_{% \delta}=\mathcal{F}_{x}^{-1}i(\coth(\delta\xi))\mathcal{F}_{x}, is considered. It is shown that the Cauchy problem of the higher-order intermediate long wave equation is locally well-posed in H 3 / 4 {H^{3/4}}. [ABSTRACT FROM AUTHOR]