The in vivo mechanics of the annulus fibrosus of the intervertebral disc is one of biaxial loading rather than uniaxial loading. The material properties of the annulus are intimately linked to the osmolarity in the tissue. This paper presents biaxial relaxation experiments of canine annulus fibrosus tissue under stepwise changes of external salt concentration. The force tracings show strong time, salt concentration and orientation dependent stresses. The force tracing signature of a response to a change in strain, is one of a jump in stress that relaxes partly as the new strain is maintained. The force tracing signature of a step wise change in salt concentration is a progressive monotonous change in stress towards a new equilibrium value. Though the number of samples does not allow any definitive quantitative conclusions, the trends may shed light on the complex interaction between directionality of forces, strains and fiber orientation on the one hand and on the osmolarity of the tissue on the otherhand. The dual response to a change in strain is understood as an immediate response before fluid flows in or out of the tissue, followed by a progressive readjustment of the fluid content in time because of the gradient in fluid chemical potential between the tissue and the surrounding solution.