Oz is a recent high-level programming language, based on an extension of the concurrent constraint model by higher-order procedures and state. Oz is a dynamically typed language like Prolog, Scheme, or Smalltalk. We investigate two approaches of making static type analysis available for Oz: Set-based failure diagnosis and strong typing. We define a new system of set constraints over feature trees that is appropriate for the analysis of record structures, and we investigate its satisfiability, emptiness, and entailment problem. We present a set-based diagnosis for constraint logic programming and concurrent constraint programming as first-order fragments of Oz, and we prove that it correctly detects inevitable run-time errors. We also propose an analysis for a larger sublanguage of Oz. Complementarily, we define an Oz-style language called Plain that allows an expressive strong type system. We present such a type system and prove its soundness.