We describe a new method for characterizing the non-linear behavior of
complex fluids at both small and large deformations. For creep measur
ements, we use the coupling between the instrumental inertia and the m
aterial's elasticity to follow the rheological behavior of a solution
of iota carrageenan both above and below the yield stress. It is shown
that this coupling selectively excites one particular frequency of th
e relaxation spectrum. An analytical calculation is used to quantify t
he non-linear behavior near the yield stress. The ''free'' oscillation
s observed during the first few seconds allow us to choose the most ap
propriate mechanical model. Comparison with experiment shows that even
above the yield stress, a linear model can still give independently r
eliable information about the changes in each element of the mechanica
l model. A comparison of free and forced oscillations in controlled st
ress rheometry shows both experimentally and theoretically the conditi
ons under which the use of free oscillations is advantageous.