Gradualism is the type of evolutionary process in which the selection for a certain trait occurs gradually, with small changes over a long period of time. This is the basis for Classic New Darwinism.
Unlike gradualism, punctuated equilibrium occurs through changes that come in spurts. Thus there are periods with little change and short periods with huge changes. This theory is best supported by the fossil record that does not contain any individuals showing transitional characteristics.
Both theories are similar in their assumption of the cause for change being natural selection as well as a common descent of all organisms.