  This paper is motivated by relations between association and independence of
random variables. It is well-known that for real random variables independence
implies association in the sense of Esary, Proschan and Walkup, while for
random vectors this simple relationship breaks. We modify the notion of
association in such a way that any vector-valued process with independent
increments has also associated increments in the new sense --- association
between blocks. The new notion is quite natural and admits nice
characterization for some classes of processes. In particular, using the
covariance interpolation formula due to Houdr\'{e}, P\'{e}rez-Abreu and
Surgailis, we show that within the class of multidimensional Gaussian processes
block-association of increments is equivalent to supermodularity (in time) of
the covariance functions. We define also corresponding versions of weak
association, positive association and negative association. It turns out that
the Central Limit Theorem for weakly associated random vectors due to Burton,
Dabrowski and Dehling remains valid, if the weak association is relaxed to the
weak association between blocks.
