An embroidery system including an embroidery frame assembly having an inner first frame (51) and an outer second frame (53), a portion of a planar formation to be processed being able to be clamped therebetween. The first frame (51) is connected by a bridge (61) to a radially outer secondary connector (57), and a connecting portion (63) of this bridge (61) bridges the second frame (53) when the latter is connected to the first frame (51). When combined with an embroidery module connected to a free arm sewing machine, the embroidery frame assembly enables in a simple manner the embroidering of pouch-type and tubular planar formations.