A separator film for a battery is formed as a hydrophilized porous biaxially oriented film. The porous biaxially oriented film has a porosity of at least about 70%, a thickness in the range of about 10 to about 500 .mu.m, and a pore size in the range of about 0.01 to about 20 .mu.m. The porous film is made of hydrophobic resin, and a hydrophilic high polymer which is fixed in the pores of the film. The hydrophilic high polymer may be heterogeneously distributed in the porous film, so that the separator film has a hydrophilic portion and a hydrophobic portion. The porosity and/or the pore size of the porous film can be varied in the direction of film thickness. The separator film is applied in an alkaline storage battery or a nonaqueous electrolyte battery such as a lithium battery.