Double degree of freedom (DDOF) linear systems are frequently used to model the aero-elastic response of slender prismatic systems until the first critical state is reached. Relevant mathematical models appearing in literature differ in principle by way of composition of aero-elastic forces. This criterion enables to sort them roughly in three groups: (i) neutral models - aero-elastic forces are introduced as suitable constants independent from excitation frequency and time; (ii) flutter derivatives - they respect the frequency dependence of aero-elastic forces; (iii) indicial functions - they are defined as kernels of convolution integrals formulating aero-elastic forces as functions of time. The paper tries to put all three groups together on one common basis to demonstrate their linkage and to eliminate gaps in mathematical formulations between 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 tunnel and full scale measurements. and Obsahuje seznam literatury