Abstract: We investigate various limits of the twistor spaces associated to the self-dual metrics on $${n \mathbb{CP}^2}$$ , the connected sum of the complex projective planes, constructed by C. LeBrun. In particular, we explicitly present the following 3 kinds of degenerations whose limits of the corresponding metrics are: (a) LeBrun metrics on $${(n-1) \mathbb{CP}^2}$$ , (b) (another) LeBrun metrics on the total space of the line bundle $${\fancyscript O(-n)}$$ over $${\mathbb{CP}^1}$$ , (c) the hyper-Kähler metrics on the small resolution of rational double points of type A n-1, constructed by G.W. Gibbons and S.W. Hawking.