  The study of Cameron-Liebler line classes in PG($3,q$) arose from classifying
specific collineation subgroups of PG($3,q$). Recently, these line classes were
considered in new settings. In this point of view, we will generalize the
concept of Cameron-Liebler line classes to AG($3,q$). In this article we define
Cameron-Liebler line classes using the constant intersection property towards
line spreads. The interesting fact about this generalization is the link these
line classes have with Cameron-Liebler line classes in PG($3,q$). Next to
giving this link, we will also give some equivalent ways to consider
Cameron-Liebler line classes in AG($3,q$), some classification results and an
example based on the example found in [3] and [6].
