Zusammenfassung: Let K be a finite field extension of Q_p. We construct the universal family of filtered (phi,N)-modules, or (more generally) the universal family of (phi,N)-modules with a Hodge-Pink lattice, and study its geometric properties. Building on this, we construct the universal family of semi-stable representations of the Galois group of K in Q_p-algebras. All these universal families are parametrized by moduli spaces which are Artin stacks in schemes or in adic spaces locally of finite type over Q_p in the sense of Huber. This has conjectural applications to the p-adic local Langlands program.