The existence of a dilaton (or moduli) with gravitational-strength coupling to matter imposes stringent constraints on the allowed energy scale of cosmic strings, $η$. In particular, superheavy gauge strings with $η\sim 10^{16} GeV$ are ruled out unless the dilaton mass $m_ϕ \gsim 100 TeV$, while the currently popular value $m_ϕ \sim 1 TeV$ imposes the bound $η\lsim 3 \times 10^{11} GeV$. 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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