We aim at considering some results on the exchangeability of a random vector and a random sequence in terms of a copula function. In particular, the special case of pairwise independent random variables is considered. In the second part of the talk we present "a measure of non-exchangeability" for pairs of identically distributed random variables by illustrating possible applications in identification of dependence structure of some stochastic models. Then we show that the random pairs satisfying some special dependence properties tend to be "more exchangeable" than others.