In this paper, we construct a hyperkähler structure on the complexification ${𝒪}^{ℂ}$ of any Hermitian symmetric affine coadjoint orbit $𝒪$ of a semi-simple $L^{*}$-group of compact type, which is compatible with the complex symplectic form of Kirillov-Kostant-Souriau and restricts to the Kähler structure of $𝒪$. By a relevant identification of the complex orbit ${𝒪}^{ℂ}$ with the cotangent space $T𝒪$ of $𝒪$ induced by Mostow’s decomposition theorem, this leads to the existence of a hyperkähler structure on $T𝒪$ compatible with...