We introduce deformations of generically log smooth families and describe their infinitesimal automorphisms. This theory works well only if the generically log smooth families under consideration have the base change property. As a variant to deal with situations where we do not have the base change property, we introduce enhanced generically log smooth families. For both the plain case and the enhanced case, we introduce systems of deformations. They are a device to fix the local deformation theory and thus simplify the deformation problem.