  Exclusive decays of $\chi_{cJ}(J=0,2)$ into $\phi\phi$ are investigated in
the framework of perturbative quantum chromodynamics(pQCD) and $\tpz$ quark
pair creation model. The results show that these two mechanisms exhibit a quite
different behavior in evaluating the decay width for the $\chi_{c0}$ and
$\chi_{c2}$. In pQCD method with nonrelativistic(NR) approximation, while the
calculated $\cxpp{2}$ decay width is comparable with measured one, the result
for the $\cxpp{0}$ decay width is suppressed and much smaller than experimental
value. However, in $\tpz$ quark pair creation model, the situation is reversed:
the decay width of $\cxpp{0}$ is greatly enhanced and can reproduce the large
measured value, while the contribution to the $\cxpp{2}$ decay width is small.
The results suggest that while the pQCD mechanism is the dominant mechanism for
$\cxpp{2}$ decay, the $\tpz$ quark pair creation mechanism is the dominant one
for $\cxpp{0}$ decay.
