While light limitation can inhibit bloom formation in dinoflagellates, the potential for high‐intensity photosynthetically active radiation (PAR) to inhibit blooms by causing stress or damage has not been well‐studied. We measured the effects of high‐intensity PAR on the bloom‐forming dinoflagellates Alexandrium fundyense and Heterocapsa rotundata. Various physiological parameters (photosynthetic efficiency Fv/Fm, cell permeability, dimethylsulfoniopropionate [DMSP], cell volume, and chlorophyll‐a content) were measured before and after exposure to high‐intensity natural sunlight in short‐term light stress experiments. In addition, photosynthesis‐irradiance (P‐E) responses were compared for cells grown at different light levels to assess the capacity for photophysiological acclimation in each species. Experiments revealed distinct species‐specific responses to high PAR. While high light decreased Fv/Fm in both species, A. fundyense showed little additional evidence of light stress in short‐term experiments, although increased membrane permeability and intracellular DMSP indicated a response to handling. P‐E responses further indicated a high light‐adapted species with Chl‐a inversely proportional to growth irradiance and no evidence of photoinhibition; reduced maximum per‐cell photosynthesis rates suggest a trade‐off between photoprotection and C fixation in high light‐acclimated cells. Heterocapsa rotundata cells, in contrast, swelled in response to high light and sometimes lysed in short‐term experiments, releasing DMSP. P‐E responses confirmed a low light‐adapted species with high photosynthetic efficiencies associated with trade‐offs in the form of substantial photoinhibition and a lack of plasticity in Chl‐a content. These contrasting responses illustrate that high light constrains dinoflagellate community composition through species‐specific stress effects, with consequences for bloom formation and ecological interactions within the plankton.