A luminescence detector with a liquid-core waveguide. For detecting photoluminescence, the exciting radiation is provided transversely instead of axially, thus eliminating the need for monochromators and focusing optics. For detecting chemiluminescence, the chemiluminescent reagents are mixed in situ in the detector, thus eliminating time loss which results in loss of chemiluminescence. A further aspect of the invention is the electrogeneration of an unstable reagent for the production of chemiluminescence. The unstable reagent is generated in such a way that there is complete separation of anodic and cathodic products without the use of a physical barrier.