The rising concern about the dependence on synthetic polymers and oil has motivated research on competitive bio-based replacement materials. Some of the often considered bio-based thermoplastics are starch, polylactic acid (PLA) and rather recently, lignin. These bio-plastics in combination with natural fibers (flax, hemp, wood) are used to manufacture whole bio-based composites. Although there are certain direct benefits to use natural fibres in composites, their performance is often very nonlinear. Moreover, properties of these materials are very sensitive to moisture and temperature. The behavior of these composites has to be studied and mechanisms occurring during the loading must be identified. The effect of temperature and relative humidity on mechanical behavior of natural fiber reinforced bio-based matrix composites subjected to the tensile loading was investigated. Time dependent behavior of these materials is analyzed. Testing methodology is suggested to identify sources of nonlinearities observed in stress-strain curves. It was found that microdamage accumulation and stiffness reduction is significant for some of the composites but the major nonlinear phenomena are related to nonlinear viscoelasticity and viscoplasticity. Material models accounting for these effects are proposed and their predictive capability is demonstrated.