Behavior of slender aero-elastic systems in a sub-critical domain including position of the lowest critical state is commonly investigated using double degree of freedom (DDOF) linear model. The most frequently used are neutral models treating aero-elastic forces as certain constants corresponding to system parameters and stream velocity. Although this approach is working well, it shows a number of shortcomings. For this reason modeling by flutter derivatives or indicial functions has been launched. However, these two groups of models have been developed separately one from each other. It seems they are rather isolated until now. Moreover they mostly suffer from various gaps in mathematical formulations and further treatment. The paper tries to put all three groups together on one common basis and to demonstrate linkage of them. This approach allows formulate more sophisticated models combining main aspects of all groups in question keeping the DDOF basis. These models correspond by far better to results of wind channel and full scale measurements. and Obsahuje seznam literatury