A non-negative transferable utility (TU) game is average monotonic if there exists a non-negative allocation according to which the relative worth is not decreasing when enlarging the coalition. We generalize this definition to the nontransferable utility (NTU) case. It is shown that an average monotonic NTU game shares several properties with an average monotonic TU game. In particular it has a special core element and there exists a population monotonic allocation scheme. We show that an NTU bankruptcy game is average monotonic with respect to the claims vector. Keywords: nontransferable utility; average monotonicity; core; population monotonicity JEL classification: C71