  We introduce the concept of $t$-spread monomials and $t$-spread strongly
stable ideals. These concepts are a natural generalization of strongly stable
and squarefree strongly stable ideals. For the study of this class of ideals we
use the $t$-fold stretching operator. It is shown that $t$-spread strongly
stable ideals are componentwise linear. Their height, their graded Betti
numbers and their generic initial ideal are determined. We also consider the
toric rings whose generators come from $t$-spread principal Borel ideals.
