Abstract : The LEP energy and luminosity increase allowed to extend considerably the search for new physics in e+e- colliders. Supersymmetry solves several problems of the Standard Model by introducing a symmetry between fermions and bosons. The stop (t1) and the sbottom (b1) squarks, supersymmetric partners of the third generation quarks could be among the lightest supersymmetric particles. Squarks have been searched in the data collected by DELPHI from 1998 to 2000 at centre-of-mass energies ranging from 189 to 208 GeV. When the R-parity is conserved, the lightest supersymmetric particle (LSP) is the neutralino (01) which interacts weakly with matter. The squarkdecay channels are t1 -> c01 and b1 -> b01. Signal events are characterised by two jets and missing energy. Special care was taken in the modelling of the stop hadronisation and in the photon-photon interactions leading to hadrons. Limits on the squarkmasses have been obtained. However, new models predict that the LSP is the gluino (g). The missing energy signature of the LSP is weakened leading to a new phenomelogy. The gluino LSP scenario has been developped and searched in DELPHI. Data collected in 1994 at the Z0 peakallowed for the first time to give a mass limit on a stable gluino. LEP2 data have been analysed to search for a stop decaying into cg and for a sbottom decaying into bg. Limits on the squarkmasses in this scenario have been obtained.