An analysis of the data collected in 1997 and 1998 with the DELPHI detector at e(+)e(-) collision energies close to 183 and 189 GeV was performed in order to extract the hadronic and leptonic fermion-pair cross-sections, as well as the leptonic forward-backward asymmetries and angular distributions. The data are used to put limit on contact interactions between fermions, the exchange of R-parity violating SUSY sneutrinos, Z' bosons and the existence of gravity in extra dimensions. (C) 2000 Published by Elsevier Science B.V.