  We look for $\Delta\Delta$ and $N\Delta$ resonances by calculating $NN$
scattering phase shifts of two interacting baryon clusters of quarks with
explicit coupling to these dibaryon channels. Two phenomenological
nonrelativistic chiral quark models giving similar low-energy $NN$ properties
are found to give significantly different dibaryon resonance structures. In the
chiral quark model (ChQM), the dibaryon system does not resonate in the $NN$
$S$-waves, in agreement with the experimental SP07 $NN$ partial-wave scattering
amplitudes. In the quark delocalization and color screening model (QDCSM), the
$S$-wave NN resonances disappear when the nucleon size $b$ falls below 0.53 fm.
Both quark models give an $IJ^P = 03^+$ $\Delta\Delta$ resonance. At $b=0.52
$fm, the value favored by baryon spectrum, the resonance mass is 2390 (2420)
MeV for the ChQM with quadratic (linear) confinement, and 2360 MeV for the
QDCSM. Accessible from the $^3D_3^{NN}$ channel, this resonance is a promising
candidate for the known isoscalar ABC structure seen more clearly in the
$pn$$\to $$d\pi\pi$ production cross section at 2410 MeV in the recent
preliminary data reported by the CELSIUS-WASA Collaboration. In the isovector
dibaryon sector, our quark models give a bound or almost bound
$^5S_2^{\Delta\Delta}$ state that can give rise to a $^1D_2^{NN}$ resonance.
None of the quark models used has bound $N\Delta$ $P$-states that might
generate odd-parity resonances.
