**The paper is published:**
European Journal of Combinatorics, May 1998

**MSC:**- 05D05 Extremal set theory
- 06A07 Combinatorics of partially ordered sets

component sum equals $l$. A subset $\mathcal{F}\subseteq N_l(n,k)$ is called a

$t$--intersecting family if every two tuples in $\mathcal{F}$ have nonzero

entries in at least $t$ common coordinates. We determine the maximum size of a

$t$--intersecting family in $N_{\lfloor \lambda n\rfloor}(n,k)$ asymptotically for

all fixed $\lambda$ ($0<\lambda