A variety of exponential models with affine dual foliations have been
noted to possess certain rather similar statistical properties. To giv
e a precise meaning to what has been conceived as ''similar'' we here
propose a set of five conditions, of a differential geometric/statisti
cal nature, that specify the class of what we term orthogeodesic model
s. It is discussed how these conditions capture the properties in ques
tion, and it is shown that some important nonexponential models turn o
ut to satisfy the conditions, too. The conditions imply, in particular
, a higher-order asymptotic independence result. A complete characteri
zation of the structure of exponential orthogeodesic models is derived
.