The concept of the Morse index characterizes the behavior near the cri
tical points of the action functional that governs physical systems. W
e study the specific feature of Morse indices for the case that there
are several number of critical points; on each of these critical point
s the Morse indices are defined. As a concrete example, we consider a
model of one-dimensional field theory model. By using the idea of the
adiabatic spectral flow, it is shown that the change of the Morse indi
ces is correlated with the structure change inherent in the solutions
of field equation that is controlled by the parameters built in the fi
eld action.