The invention describes novel formulations of nonsteroidal anti-inflammatory drugs (NSAIDs) based on complex aggregates with at least three amphipatic components suspended in a suitable, e.g. pharmaceutically acceptable, polar liquid medium. A suitably ionised NSAID is one of the two, amongst said three, components that tends to destabilise lipid membranes, the other system component with such activity being typically a surfactant. In contrast, the remaining amongst said at least three amphipatic components typically forms a stable lipid membrane on it's own. An essential characteristics of the resulting, relatively large, aggregates is an improved ability to penetrate pores, in a semi-permeable barrier, at least 30%, and often much smaller than the average diameter of the complex aggregate. This enables said aggregates to mediate NSAID transport through semi-permeable barriers including mammalian skin. As a result of the skin penetration by NSAID loaded large aggregates, the drug delivered transcutaneously with such carriers gets deeper into the tissue than the corresponding NSAID from a solution on the skin surface. This is believed to be due to the special ability of suitable large carriers to bypass the local sink of blood capillaries at the epidermal-dermal junction in the skin. The carrier-mediated delivery of locally applied NSAIDs thus allows therapy of deep tissues under the drug administration site, which is medically highly desirable.