Patterns of invasion by the seaweeds Grateloupia turuturu Yamada and Sargassum muticum (Yendo) Fensholt under crossed combinations of the regime (mean intensity and temporal variability) of climate-related mechanical disturbance and constant nutrient enrichment were experimentally examined in rockpools in north Portugal. The cover of both species was larger under high compared to low intensity of disturbance, but this effect was enhanced by events more heterogeneously distributed over a period of 19 months. The invasion by G. turuturu was also larger in enriched pools, but only when disturbance was applied at high intensity. The richness of native taxa was increased by high intensity events of disturbance evenly distributed over time and by low intensity events heterogeneously distributed, while no differences were documented for other treatments. Temporal variability of disturbance and nutrients interactively affected the total cover of native taxa and the availability of bare rock in different directions. Enriched conditions increased the space occupancy by natives and reduced substratum availability only when associated to heterogeneous events of disturbance. At the same time, relatively more variable disturbances caused a reduced cover by native taxa and an increased availability of free space, but only under natural nutrient levels. Present findings contribute to understand the conditions that would be more likely to facilitate the spread of G. turuturu and S. muticum under current and predicted scenarios of compounded environmental changes and in relation to traits of recipient systems that are considered relevant for the success of invasions, including the native richness and the degree of usage of resources, i.e. primarily space.