  We first develop a method to calculate a complete set of mode functions which
describe the quantum fluctuations generated in one-bubble open inflation
models. We consider two classes of models. One is a single scalar field model
proposed by Bucher, Goldhaber and Turok and by us as an example of the open
inflation scinario, and the other is a two-field model such as the
``supernatural'' inflation proposed by Linde and Mezhlumian. In both cases we
assume the difference in the vacuum energy density between inside and outside
the bubble is negligible. There are two kinds of mode functions. One kind has
usual continuous spectrum and the other has discrete spectrum with
characteristic wavelengths exceeding the spatial curvature scale. The latter
can be further devided into two classes in terms of its origin. One is called
the de Sitter super-curvature mode, which arises due to the global spacetime
structure of de Sitter space, and the other is due to fluctuations of the
bubble wall. We calculate the spectrum of quantum fluctuations in these models
and evaluate the resulting large angular scale CMB anisotropies. We find there
are ranges of model parameters that are consistent with observed CMB
anisotropies.
