The assessment of mediation is important for testing the mechanisms that explain an observed relationship between exposure and disease. Several types of direct and indirect effects have been defined, broadly characterized as either controlled or natural. The identification of these effects requires a stricter set of assumptions than those necessary for the identification of the total effect of exposure on disease. The particular assumptions that are required differ depending on the type of effect. We use an approach based on response types to derive new assumptions for the identification of direct and indirect effects, both controlled and natural. These assumptions are stated in terms of response types and potential outcomes, and are compared with those already in the literature. This approach yields an alternative, and sometimes less stringent, set of assumptions for the identification of direct and indirect effects than those previously proposed.