A new class of tests is presented for testing the hypothesis of no second order interaction in three-way contingency tables. This hypothesis is expressed first in the form of linear contrasts in logarithms of the parameters of a multinomial experiment and the test is based on the general theory of locally asymptotically most stringent tests. Specific test criteria are then given for testing no second order interaction in 2 × 2 × 2, 2 × 2 ×KandI×J×Kcontingency tables. Two examples are discussed.