For a two-way contingency table with an explanatory and a response variables, Tomizawa, Seo and Ebi (1997) proposed a measure which describes the proportional reduction in variation from the marginal distribution to the conditional distributions of the response. Also, Tomizawa and Ebi (1998) extended this measure into a multi-way contingency table with only one response variable (and the multiple explanatory variables). This paper extends these measures into a multi-way contingency table with multiple L (L ≥ 2) response variables (and the multiple explanatory variables), which have nominal categories. Examples are given.