Inherent Case is understood as Case, the assignment of which has to be accompanied by theta-assignment (Chomsky 1995). While Nominative on the subject and Accusative on the direct object are typical representatives of structural Case, Genitive or Dative are usually taken as representatives of inherent Case. In this paper I first review the properties of ditransitive verbs in Czech explored in Dvořák (in press) who argues that there are two types of inherent Datives in Czech: a high Dative assigned by an applicative head and associated with a recipient/benefactive theta-role, and a low Dative associated with a path theta-role. I provide the evidence for the independent existence of both of these Datives outside of ditransitives: in unaccusative structures and in structures with only a dative object. After that I draw my attention to the properties of the postnominal Genitive in Czech, especially the Genitive that is assigned to the direct object of nominalized ditransitive verbs. Even though these constructions reveal that Genitive is similar to Dative in terms of the local relationship between the Case-assigning head and the Case-assigned DP, I show that we do not need to refer to Genitive’s “inherentness” in order to derive the fact that the Genitive DP always immediately follows the assigning noun. I employ the data from nominalized ditransitives, in which the theta-marking and Case-marking of the object DP is dissociated, complemented by data on nominalizations with small clause subjects in Genitive, to argue for the “structuralness” of the postnominal Genitive in Czech.