  Exclusive measurements of the $pp \to pp\pi^0\pi^0$ reaction have been
performed at CELSIUS/WASA at energies from threshold up to $T_p$ = 1.3 GeV.
Total and differential cross sections have been obtained. Here we concentrate
on energies $T_p \ge$ 1 GeV, where the $\Delta\Delta$ excitation becomes the
leading process. No evidence is found for a significant ABC effect beyond that
given by the conventional $t$-channel $\Delta\Delta$ excitation. This holds
also for the double-pionic fusion to the quasibound $^2$He. The data are
compared to model predictions, which are based on both pion and $\rho$
exchange. Total and differential cross sections are at variance with these
predictions and call for a profound modification of the $\rho$-exchange. A
phenomenological modification allowing only a small $\rho$ exchange
contribution leads to a quantitative description of the data.
