New concepts of generalized (ρ,θ)-η invex functions for non-differentiable functions and generalized (ρ,θ)-η invariant monotone operators for set-valued mappings are introduced. The relationships between generalized (ρ,θ)-η invexity of functions and generalized (ρ,θ)-η invariant monotonicity of the corresponding Clarke's subdifferentials are studied. Some of our results are extension and improvement of some results obtained in (Jabarootion and Zafarani (2006); Behera et al. (2008)).