In a certain unfavourable environment, a single DNA molecule undergoes a conformational transition from an expanded coil state to a collapsed form. Here, this transition is induced by poly(ethylene glycol) (PEG) in a solvent mixture composed of an aqueous salt buffer and methanol. A theoretical description is presented in terms of the free energy of mixing DNA, PEG, and solvent, the elastic part of the free energy for DNA chains, and the translational entropy of the low molecular ions. Further effects taken into account are DNA-counterion binding and solvent quality. The theoretical predictions are: (1)The transition between the coil and the collapsed state is discontinuous. There exists a coexistence region where both states coexist side by side, but its width is very small. (2) The collapse takes place at a certain critical PEG concentration C-PEG,C-c. The value of this PEG-concentration depends on the degree of PEG polymerisation, P-w,P-PEG, the molar fraction, X-methanol, Of methanol, and on the concentration, c(salt), of the added salt. For given values of X-methanol and c(salt), C-PEG,C-c, decreases with increasing P-w,P-PEG. That is, it is easier to induce the DNA collapse with PEG of high molar mass than with PEG of low molar mass. If both P-w,P-PEG and c(salt) are constant, C-PEG,C-c increases as the methanol concentration decreases. This means that addition of methanol promotes DNA condensation. If finally P-w,P-PEG and X-methanol are chosen constant, C-PEG,C-c decreases as c(salt) increases. Thus we can say, the collapsed DNA state is the more stabile the higher are P-w,P-PEG, X-methanol as well as c(salt). That is, these three parameters act synergistically. (3) Theory gives some information about the DNA-molecule size. While in the coil state the expansion factor, ct, is of the order of 1.8-2.4, it is of the order of 0.3 in the compact state. Results of measurements presented in the companion paper affirm these results.