  In this paper we make a detailed comparison between the Paley-Wiener theorems
of J. Arthur and P. Delorme. We prove that these theorems are equivalent from
an a priori point of view. We also give an alternative formulation of the
theorems in terms of the Hecke algebra of bi-K-finite distributions supported
on K. Our techniques involve derivatives of holomorphic families of continuous
representations and Harish-Chandra modules.
