The present invention provides a method of treating lysosomal storage diseases such as Hurler syndrome and Batten disease in individuals in need of such treatment, comprising the step of administering to said individuals a therapeutically effective dose of an aminoglycoside. In addition, this method may further comprise treating the individual with enzyme replacement therapy. Furthermore, the present invention provides method of pharmacologically suppressing premature stop mutations in an individual with these lysosomal storage diseases, comprising the step of administering to said individual a pharmacologically effective dose of an aminoglycoside.