In applications tail dependence is an important property of a copula. It characterizes the degree of dependence between marginals in the tail area. Bivariate tail dependence is investigated in many papers, but multivariate tail dependence has not been studied widely. The aim of this paper is to introduce a measure of the tail dependence for n-dimensional copulas. We have defined multivariate upper and lower tail dependence coefficients as limits of the probability that values of one marginal will be large if at least one of other marginals will be as large also. Further we have derived some relations between introduced tail dependence and bivariate tail dependence coefficients. Applications have shown that the multivariate t-copula has been successfully used in practice because of tail dependence property. Therefore we have paid attention to the properties of the introduced tail dependence coefficient for t-copula and examined it by the simulation technique.