Every two-term complex of coherent sheavesformula_95on a scheme formula_96 has a canonical sheaf of groupoids associated to it, where on an open subset formula_97 there is a two-term complex of formula_98-modulesformula_99giving a groupoid. It has objects given by elements formula_100 and a morphism formula_101 is given by an element formula_102 such thatformula_103In order for this stack to be a Gerbe, we must have the cohomology sheaf formula_104 to always have a section. This hypothesis implies the category constructed above always has objects. Note this can be applied to the situation of comodules over Hopf-algebroids to construct algebraic models of gerbes over affine or projective stacks (projectivity if a graded Hopf-algebroid is used). In addition, two-term spectra from the stabilization of the derived category of comodules of Hopf-algebroids formula_105 with formula_106 flat over formula_107 give additional models of gerbes which are non-strict.