Link to this article: http://journals.cambridge.org/abstract_S0305004110000174 How to cite this article: JOSE M. GARCÍA-CALCINES, PEDRO R. GARCÍA-DÍAZ and ANICETO MURILLO MAS (2010). The Ganea conjecture in proper homotopy via exterior homotopy theory. Mathematical AbstractIn this article we provide sufficient conditions on a space X to verify Ganea conjecture with respect to exterior and proper Lusternik-Schnirelmann category. For this aim we previously develop an exterior version of the Whitehead, cellular approximation, CWapproximation and Blakers-Massey theorems within a homotopy theory of exterior CWcomplexes and study their corresponding analogues and consequences in the proper setting.