In a study of the reaction e(-)e(+)-> W-W+ with the DELPHI detector, the probabilities of the two W particles occurring in the joint polarisation states transverse-transverse (T T), longitudinal-transverse plus transverse-longitudinal (LT) and longitudinal-longitudinal (LL) have been determined using the final states WW -> lvq (q) over bar (l = e, mu). The two-particle joint polarisation probabilities, i.e. the spin density matrix elements rho T T, rho LT, rho LL, are measured as functions of the W- production angle, theta(W-), at an average reaction energy of 198.2 GeV. Averaged over all cos.W-, the following joint probabilities are obtained: (rho) over barT T = (67 +/- 8)%, (rho) over barL T = (30 +/- 8)%, (rho) over barL T = (3 +/- 7)%. These results are in agreement with the Standard Model predictions of 63.0%, 28.9% and 8.1%, respectively. The related polarisation cross-sections sigma(TT), sigma(LT) and sigma(LL) are also presented.