In a recent paper spaces of holomorphic functions on tubes inwhich generalize the HardyHpspaces on tubes were defined and studied using the theory of ultra-distributions. UsingLptheory of Fourier transforms Cauchy and Poisson integral representations of these functions were obtained and existence ofS′(Mk;Mk)-boundary values of generalizedHp-functions was established for 1 <p≤ 2. In this paper some of these results are extended to the case 2 <p< ∞. A Poisson integral representation is given and a sufficient condition for a function in the generalized space to be inHp-space is obtained in terms of itsS′(Mk;Mk)-boundary value.