While RHEED observations show that 10 to 11 Angstrom is the stability limit for an open bcc Co layer when grown on an Fe substrate, our XRD and NMR studies have shown that, in MBE grown Co/Fe superlattices, cobalt can be stabilised in a bcc structure up to a critical Co thickness of 21 Angstrom. In order to understand this apparent discrepancy, NMR experiments have been carried out in Co-x/Fe-y multilayers with thickness varying in the range 5 Angstrom < x < 42 Angstrom and 24 Angstrom < y < 60 Angstrom, grown on GaAs (110) as well as on MgO (100) substrates. The analysis of the chemical short range order by NMR concludes that the larger bcc Co thickness observed in superlattices results from the formation of a rather homogeneous CoFe20% bcc alloy which contains the supplementary 10-11 Angstrom of Co and which coexists with pure Co grains. The concentration of about 20% Fe in the alloyed part of the Co layer happens to be close to the stability limit for a bcc structure in the equilibrium phase diagram of bulk CoFe alloys. However, while a mixture of bcc and fee phases is observed in bulk alloys, the bcc structure is preserved in all phases under the MBE growth conditions and below the critical thickness. Above the critical thickness a mixture of bcc Co, bcc CoFe and hcp Co is observed.