  Beligiannis and Marmaridis [\emph{Comm. in Algebra,} 22(12)(1994), 5021-5036]
constructed the left and right triangulated structures on the stable categories
of additive categories induced from some homological finite subcategories. We
extend their results to slightly more general settings. As an application of
our results we give some new examples of stable categories which have left or
right triangulated structures from abelian model categories. An interesting
outcome is that we can describe the pretriangulated structures of the homotopy
categories of abelian model categories via the ones of stable categories.
