This dissertation investigates the syntax of case(-value)-assignment (κ-ASSIGNMENT) and Phi(-feature)-agreement (Φ-AGREEMENT) in nominal and verbal domains, with an emphasis on nomino-verbal infinitives and their cross-clausal dependencies, examining Kashmiri before extending to Hungarian. Although unrelated, both languages exhibit typological parallels in person-based differential object coding, inflected infinitives that index their own arguments, and pseudo-long-distance agreement between matrix verbs and infinitivally embedded arguments. Chapter 1 introduces the dissertation’s empirical scope, while Chapter 2 outlines its modified Minimalist theoretical approach to the data. Chapter 3 presents the internal syntax of Kashmiri nominals assumed in subsequent chapters about nominal interactions with the verbal domain. Chapter 4 proposes new analyses of the aspectual alignment split in Kashmiri root clauses (ergative–absolutive in perfectives vs. nominative–accusative/dative in non-perfectives), and of person hierarchy effects (PHEs) in κ-assignment to objects in non-perfectives. Chapters 5, 6, and 7 survey the syntax of Kashmiri infinitival constructions, covering subject-control, object-control, and non-control, respectively. I explore the degree to which PHEs emerge in infinitival clauses, and identify the range of flavors that Inf, the head of an Inf(initive)P immediately dominating vP, assumes as a κ-assigner and/or Φ-agreement locus. Chapter 8 examines the interaction between PHEs and scope-marking across finite clause boundaries in Kashmiri long-distance WH-questions. Chapters 9, 10, and 11 extend the formalism to Hungarian nominals, root clauses, and embedded clauses, respectively, proposing that Hungarian PHEs arise only at PF (in the morphological exponence rather than the syntactic mechanism of agreement), besides addressing pseudo-long-distance agreement, overt realization of focused PRO in subject-control constructions, and dative postpositional subjects in non-control constructions. Chapter 12 summarizes the dissertation’s findings and suggests directions for future research. To capture the languages’ patterns of case and agreement, I modify the Minimalist framework (Chomsky 2000) to formally vary the timing with which κ and Φ-features are deactivated or lose the ability to engage in syntactic operations after valuation. Prototypically, in Φ-agreement, an uninterpretable uΦ probe on a verbal head copies a value from an interpretable iΦ goal on a nominal phrase; in structural κ-assignment, a verbal assigner head generates a value for a nominal phrase’s uninterpretable uκ. Following Bobaljik (2008b) and Preminger (2014), I abandon standard Minimalism’s reduction of structural κ-assignment to a reflex of Φ-agreement. Not only are the operations discrete in Syntax, but structural κ-assignment must precede Φ-agreement when a head can initiate both. The ability of iΦ features to participate in agreement (AGREEABILITY) depends on activation by a co-occurring κ on the same phrase. After κ is valued by κ-assignment, its iΦ-activatorhood undergoes instant or delayed extinguishment (DEACTIVATORIZATION). Instant deactivatorization is canonical when uκ is oblique (e.g., [DAT]). It simultaneously deagreeabilitizes the iΦ features and precludes their agreement with the assigner’s uΦ probes (which thus require default valuation). Alternatively, κ can be marked for delayed deactivatorization, which is canonical when uκ is non-oblique (e.g., [NOM], [ACC]). The iΦ features are kept agreeable until they have agreed with the assigner’s uΦ probes, upon which κ is deactivatorized. After valuation by agreement, uΦ features can undergo instant or delayed DEAGREEABILITIZATION. Delayed deagreeabilitization permits a former uΦ probe to serve as a goal for another uΦ probe in one more cycle of agreement, while instant deagreeabilitization prevents it from doing so. Φ-values can thus propagate from a nominal phrase to an infinitive or matrix verb that has not established a direct agreement relation with that nominal.