We address the question of finding stable and metastable cosmic strings in quasi-realistic heterotic M-theory compactifications with stabilized moduli. According to Polchinski's conjecture, the only stable strings in the absence of massless fields are Aharonov-Bohm strings. Such strings could potentially be created in heterotic compactifications as bound states of open membranes, five-branes wrapped on four-cycles and solitonic strings. However, in generic compactifications, the process of

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... i stabilization can conflict production of Aharanov-Bohm strings. In this case, heterotic cosmic strings will have to be unstable under breakage on monopoles. We estimate the monopole masses and find that they are big enough so that the strings can be metastable with a sufficiently long lifetime. On the other hand, if we allow one or more axions to remain massless at low energies, stable global strings can be produced.