We study possible bound states of the Delta Delta and Delta Delta Delt
a systems by using a two-body interaction derived from the chiral quar
k cluster model. The systems of two and three deltas, which will appea
r in nature as dibaryon and tribaryon resonances with zero strangeness
, have large similarities with the corresponding two- and three-nucleo
n systems. The two deepest bound Delta Delta states are those with ang
ular momentum and isospin (j, i) = (1, 0) and (j, i) = (0, 1) which ha
ve the same quantum numbers as the S-3(1)-D-3(1) (deuteron) and S-1(0)
(virtual) NN states. Similarly, the more strongly bound Delta Delta D
elta state is that with angular momentum and isospin (J, I) = (1/2, 1/
2) which has precisely the same quantum numbers as the triton.