In [5] Phillips proved that one can obtain the additive group of any nonstandard model *ℤ of the ring ℤ of integers by using a linear mod 1 function h : F ℚ, where F is the α-dimensional vector space over ℚ when α is the cardinality of *ℤ. In this connection it arises the question whether there are linear mod 1 functions which are neither addition nor quasi-linear. We prove that this is the case.