In the paper a new class of linear operators was introduced: linear operator B is said to be right-side hyperbolic, if operators B-l I are right-sided invertible for any l from a neighborhood of the unit circle and moreover one can specify right-side resolvent Rr(B;l ) namely a family of right inverse to B-l I analytic in l . In the paper general form of right-side resolvents is given. We also discuss a distinguishes with the hyperbolic case.