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The classification of affine line bundles on a compact complex space is a difficult problem. We study the affine analogue of the Picard functor and the representability problem for this functor. Let    be a compact complex space with   . We introduce the affine Picard functor    which assigns to a complex space    the set of families of linearly   -framed affine line bundles on    parameterized by   . Our main result states that the functor    is representable if and only if the map    is constant. If this is the case, the space which represents this functor is a linear space over    whose underlying set is   , where    is a Poincaré line bundle normalized at   . The main idea idea of the proof is to compare the representability of    to the representability of a functor considered by Bingener related to the deformation theory of   -cohomology classes. Our arguments show in particular that, for    = 1, the converse of Bingener’s representability criterion holds

Classifying affine line bundles on a compact complex space