We　generalize　the　signless　Laplacian　matrices　for　graphs　to　the　signless　Laplacian　tensors　for　even　uniform　hypergraphs　and　set　some　fundamental　properties　for　the　spectral　hypergraph　theory　based　upon　the　signless　Laplacian　tensors.　In　particular,　the　smallest　and　the　largest　Z-eigenvalues　of　the　signless　Laplacian　tensor　for　an　even　uniform　hypergraph　are　studied,　and　as　an　application,　the　bounds　of　the　edge　cut　and　the　edge　connectivity　of　the　hypergraph　involving　these　two　Z-eigenvalues　are　presented.　©　2013　John　Wiley　&　Sons,　Ltd.