The purpose of this paper is to study extendibility and stable extendibility of vector bundles over real projective spaces. We determine a necessary and sufficient condition that a vector bundle ξ over the real projective n-space RP
n is extendible (or stably extendible) to RP
m for every m>n in the case where ξ is the complexification of the tangent bundle of RP
n and in the case where ξ is the normal bundle associated to an immersion of RP
n in the Euclidean (n+k)-space R
n+k or its complexification, and give examples of the normal bundle which is extendible to RP
N but is not stably extendible to RP
N+1
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