A number of valved quartz glass ³He spin filter cells have been repeatedly exposed to various external magnetic fields in order to determine the influence of induced wall magnetization on the relaxation time in the cells. The procedures of magnetizing and degaussing of cells are described. A comparison of T₁ measurements performed in the same cell by different methods attest the good reliability of the measurements as well as the time stability of T₁ in Cs-coated quartz glass cells. No orientation dependence of the relaxation in fields of 8 G was observed. A strong dependence of T₁ on the strengths of external magnetic fields, applied perpendicular to the direction of the guide field used during the measurements, was observed at low and moderate fields. T₁ decreases rapidly by increasing the field strength up to values of about 1 kG both in Cs-coated and bare-wall cells. Further increase in the field to 7 kG has no significant influence on the relaxation value, suggesting the saturation of the cell magnetization. Macroscopic magnetization produced in the bulk of the glass as well as Cs-caused magnetization on the surface are proposed to be two different relaxation mechanisms present in the cells. The magnetization induced in cells has been determined independently of the ³He relaxation by SQUID measurements. The influence of Cs coating and of heating on T₁ in magnetized cells is discussed.