In 1949 he habilitated with the thesis Sein, Wahrheit und Wert in der heutigen Philosophie.
Except for two stays at as a visiting professor in 1962/63 and 1964 at the University of Pennsylvania he remained in Munich and ran there a center for analytical philosophy until his retirement in 1990.
In his inaugural lecture at the University of Innsbruck, he outlined the four problems in epistemology, which he focussed on in his later work: In his books Das Wahrheitsproblem und die Idee der Semantik (The Problem of Truth and the idea of Semantics, 1957), and Unvollständigkeit und Unentscheidbarkeit (Incompleteness and Undecidability, 1959) Stegmüller disseminated the ideas of Alfred Tarski and Rudolf Carnap on semantics and logics as well as those of Kurt Gödel on mathematical logic.
Later similar works are on Die Antinomien und ihre Behandlung (Antinomies and Their Treatment, 1955) as well as Strukturtypen der Logik (Types of Structures of Logic, 1961).
He demonstrates that any search for epistemological fundamentals will necessarily lead to the problem of the evidence — which Stegmüller does not regard as solvable.
In "Der Phänomenalismus und seine Schwierigkeiten" (1958), he describes the extreme problems, which hinder a stringent implementation of the phenomenalism program.