A formulation is given for a bead-spring model which possesses the following features simultaneously : (i) the Hookean springs may have different spring moduli, (ii) the friction coefficients belonging to the beads may be different, (iii) preaveraged hydrodynamic interaction may be included and (iv) the geometry of the bead-spring structure may contain cycles. The possible presence of cycles implies that one may use, in principle, three different representations for describing the geometry : one bead position representation and two different connector vector representations : one related to the springs of the entire bead-spring structure and the second related to the springs of a particular substructure (the spanning tree) of the entire bead-spring structure. For these three representations it was possible to derive the equations of motion and the expressions for the corresponding modified Rouse- and Kramers matrices. In case of a dilute solution of equal Hookean bead-spring structures (the spring moduli and friction coefficients may be non-equal, preaveraged hydrodynamic interaction may be included and the geometry may contain cycles) an explicit constitutive equation is obtained. The model is formulated in such a way that further extensions and modifications are relatively simple to incorporate.