  We investigate various limits of the twistor spaces associated to the
self-dual metrics on n 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 metrics are: (a) LeBrun
metrics on (n-1) CP ^2$, (b) (Another) LeBrun metrics on the total space of the
line bundle O(-n) over CP ^1 (c) The hyper-Kaehler metrics on the small
resolution of rational double points of type A_{n-1}, constructed by Gibbons
and Hawking.
