NOVELTY - Reactivating a catalyst involves providing a catalyst partially deactivated by fouling agent(s), contacting the catalyst with a fluid reactivating agent that is at or above its critical point and is of density to dissolve impurities, reacting the fluid reactivating agent with fouling agent, removing the fouling agent from the fluid reactivating agent, and recycling the fluid reactivating agent.    USE - Reactivating a catalyst, e.g. solid or liquid catalyst, useful for catalyzing an alkylation reaction, a transesterification reaction, an esterification reaction, an oligomerization reaction, a polymerization reaction or an isomerization reaction.    ADVANTAGE - The method effectively reactivates a catalyst regardless of the reactor type that is used for the actual process.    DETAILED DESCRIPTION - Reactivating a catalyst involves:    (a) providing a catalyst that is at least partially deactivated by at least one fouling agent and that comprises a solid catalyst or a liquid catalyst,    (b) contacting the catalyst with a fluid reactivating agent that is at or above its critical point and is of density to dissolve impurities,    (c) reacting the fluid reactivating agent with at least one fouling agent,    (d) releasing the fouling agent from the catalyst,    (e) removing the fouling agent from the fluid reactivating agent, and    (f) recycling the fluid reactivating agent.    An INDEPENDENT CLAIM is also included for a system for reactivating a catalyst, which comprises:    (i) at least one reactor for holding at least one catalyst that is partially deactivated by fouling agents,    (ii) a first pumping device (3) to direct a fluid reactivating agent toward the catalyst,    (iii) pressure and temperature control devices (5, 7) for generating pressure and temperature conditions while that catalyst is in contact with the fluid reactivating agent such that agent is at or above its critical point and is of density to dissolve the impurities,    (iv) a second pumping device coupled to direct contaminated fluid reactivating agent to a reactivating agent recovery and    (v) a third pumping device configured and operably coupled to recirculate clean fluid reactivating agent from the reactivating agent recovery to the reactor.    DESCRIPTION OF DRAWING(S) - The figure schematically shows a two-column system in which the catalyst in reactor 2 is reactivated whereas alkylation takes place in reactor 1.    Pumping device (3)    Pressure and temperature control devices (5, 7)    Active flow lines (14, 16, 18, 20)