Radially peaked density profiles were found in discharges heated purely withECH in the currentless W7-AS stellarator. Changes in the central particlesource are not significant and do not explain the density peaking. This isevidence for inward convection in W7-AS. The existence of the inwardconvection is confirmed with two independent transient transport studies.Flatness of the temperature profiles is essential for the density peaking, andan anti-correlation was found between the density and temperature gradients.The density peaks as the ECH-deposition is moved outwards. The density peakingparameter was found to decrease with increasing heating power. No cleardensity dependence was found. Strong gas puffing, or the corresponding highedge density prevents the formation of the peaked profiles.