In conventional Data Envelopment Analysis (DEA) models it has been assumed that each measure status is considered input or output. However, a performance measure in some cases can have input role for some DMUs and output role for others and is known as flexible measure. In this paper new radial FNDEA-R models are proposed in the presence of flexible measures based on the ratio of input components to output components or vice versa in the input and output orientation under constant returns to scale in general two-stage network. In our proposed models, flexible measures are determined as input or output to improve performance to maximize the relative efficiency of the DMU under evaluation. The FNDEA-R models versus FNDEA models prevent efficiency underestimation and pseudo inefficiency issues. The status of one flexible measure in the input-oriented and output-oriented FNDEA-R models may have different conclusions. The radial FNDEA and FNDEA-R models have units-invariant. A numerical example is used to illustrate the procedures.