We give a rigorous proof of mean-field critical behavior for the susceptibility (7 = 1/2) and the correlation ength (v = 1/4) formodels of lattice trees and lat- tice animals in two cases: (i) for the usual model with trees or animals construc- ted from nearest-neighbor bonds, in sufficiently high dimensions, and (ii)for a
class of "spread-out" or long-range models in which trees and animals are con- structed from bonds of various engths, above eight dimensions.