Actin filaments and microtubules are major dynamic components of the cytoskeleton of eukaryotic cells. Assembly of these polymers from monomeric actin or tubulin occurs with expenditure of energy, because ATP (or GTP) tightly bound to actin (or tubulin) is irreversibly hydrolysed during polymerization. Therefore, actin filaments an microtubules are dissipative structures. Our purpose has been to understand how the dissipation of chemical energy perturbs the laws of reversible helical polymerization defined by Oosawa, and affects the dynamics of these polymers. A kinetic study has shown that nucleotide is hydrolysed on the polymer within at least two steps consecutive to the incorporation of the monomer: cleavage of the γ-phosphoester bond followed by the slower release of P
i
; only the second reaction appears reversible. P
i
release, and not cleavage of the γ-phosphate, is linked to the destabilization of protein-protein interactions in the polymer, and therefore plays the role of a conformational switch. The dynamic properties of the polymer in the NTP- and NDP-P
i
intermediate states of the assembly process have been investigated using non-hydrolysable analogues of nucleotides and structural analogues of P
i
, AIF
4
-
and (BeF
3
-
, H
2
O). Because nucleotide hydrolysis is uncoupled from polymerization, actin filaments and microtubules grow with a ‘cap’ of terminal NTP- and NDP-P
i
- subunits that interact strongly, and prevent the rapid depolymerization of the unstable core of the polymer formed of NDP-subunits. The fact that the dynamic properties of the polymer are affected by bound nucleotide results in a nonlinear dependence of the rate of elongation on monomer concentration. This nonlinearity accounts for the dynamic instability behaviour of microtubules, which is an important feature of their function, and explains the oscillatory polymerization kinetics in a population of synchronized microtubules. The above analysis provides the basis for anticipating possible modes of regulation of cytoskeletal assembly via modulation of the rate of nucleotide hydrolysis. The role of the metal ion (Ca
2+
, Mg
2+
) chelated to the β- and γ-phosphates of ATP (or GTP) and the stereochemistry of nucleotide binding to actin and tubulin have been studied using the CrATP and CrGTP β γ-bidentate analogues of MgATP and MgGTP. The changes in the environment of the triphosphate moiety of the nucleotide following the release of P
i
; on Factin, and of Mg
2+
and P
i
; on microtubules, is proposed as being part of the conformational switch leading to the destabilization of the polymers.