Some colloidal suspensions with a thixotropic behavior and yield stress also display a minimum stress in their flow curves. One of these is an aqueous suspension of synthetic clay, consisting of anisotropic particles of nanometric size, forming a transparent thixotropic gel. Four flow regimes corresponding to four different states of strain field were defined by combining visualization techniques and rheometric measurements in cone-plate geometry. Links with the microstructure of the suspension are suggested. Flow instabilities such as localized shear and stick slip were identified in the falling branch of the flow curve and in the minimum stress area. Two regimes involving the bulk properties of the sample were identified. Consequently, proper procedures for characterizing the thixotropy of the suspensions are proposed.