We investigate the simultaneous uniformly holomorphic continuation of the uniformly holomorphic functions defined in a domain spread of uniform type, (X, θ{symbol}), over a locally convex Hausdorff space E. We construct the envelope of uniform holomorphy of (X, θ{symbol}) with an analogous method of the results of M. Schottenloher (Portugal. Math. 33 (1974)). Finally, we use this construction to the problem of extending uniformly holomorphic maps f: (X, θ{symbol}) → F, with values in a complete locally convex space to the envelope of uniform holomorphy of X. © 1987.1232448454Coueré, Analytic Functions and Manifolds in Infinite Dimensional Spaces (1974) Mathematics Studies, 11. , North-Holland, AmsterdamDineen, Holomorphically Complete Locally Convex Topological Vector Spaces (1971) Séminaire P. Lelong, , Springer-Verlag, BerlinJ. Mujica, Domains of holomorphy in (DFC)-spaces “Functional Analysis, Holomorphy and Approximation Theory,” Lecture Notes in Math., Vol. 843, Springer-Verlag, BerlinNachbin, Uniformité d'holomorphie et type exponential (1971) Séminaire P. Lelong, 205, pp. 216-224. , 1970, Lecture Notes in Math., Springer-Verlag, BerlinNachbin, Recent developments in infinite dimensional holomorphy (1973) Bulletin of the American Mathematical Society, 79 (4), pp. 625-640Noverraz, (1973) Pseudo-convextité polynomiale et domaines d'holomorphie en dimension infinie, , North-Holland, AmsterdamSchaefer, (1970) Topological Vector Spaces, , Springer, New YorkSchottenloher, Riemann domains, “Basic Results and Open Problems” (1973) Proc. on Infinite Dimensional Holomorphy, 364, pp. 196-212. , Lecture Notes in Math., Springer-Verlag, BerlinSchottenloher, Analytic continuation and regular classes in locally Hausdorff spaces (1974) Portugal. Math., 33