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The existence of a dilaton (or moduli) with gravitational-strength coupling to matter imposes stringent constraints on the allowed energy scale of cosmic strings, . In particular, superheavy gauge strings with $\eta \sim 10^{16} GeVm_{\phi} \gsim 100 TeV$, while the currently popular value imposes the bound $\eta \lsim 3 \times 10^{11} GeV$. Similar constraints are obtained for global topological defects. Some non-standard cosmological scenarios which can avoid these constraints are pointed out.

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