In general, the notions of lack of stability and lack of uniqueness ar
e not equivalent. This question is briefly discussed in the case of so
il behaviour. By utilising an incrementally nonlinear model and variou
s types of loading paths (i.e. proportional loading and with multiple
bends) stability and uniqueness are more precisely investigated in the
case of undrained paths on loose sands. The theoretical results are a
lso analysed with respect to the convergency of the response curves wh
en the length of bends decreases. It is then shown that some conclusio
ns obtained in the case of undrained loading can be generalised for a
large class of stress paths.