[Authors] O. I. Reinov [Title] Approximation properties associated with quasi-normed operator ideals of $(r,p,q)$-nuclear operators [AMS Subj-class] 46B28 Spaces of operators; tensor products; approximation properties [Abstract] We consider quasi-normed tensor products lying between Laprest\'e tensor products and spaces of $(r,p,q)$-nuclear operators. We define and investigate the corresponding approximation properties for Banach spaces. An intermediate aim is to answer a question of Sten Kaijser. [Comments] LaTeX, English, 9 pp. [Contact e-mail] orein51@mail.ru