Recently Ding et al. [Phys. Rev. B 95, 184404 (2017)] reported that their nuclear magnetic resonance (NMR) study on EuCo$_2$As$_2$ successfully characterized the antiferromagnetic (AFM) propagation vector of the incommensurate helix AFM state, showing that NMR is a unique tool for determination of the spin structures in incommensurate helical AFMs. Motivated by this work, we have carried out $^{153}$Eu, $^{31}$P and $^{59}$Co NMR measurements on the helical antiferromagnet EuCo$_2$P$_2$ with an AFM ordering temperature $T_{rm N}$ = 66.5 K. An incommensurate helical AFM structure was clearly confirmed by $^{153}$Eu and $^{31}$P NMR spectra on single crystalline EuCo$_2$P$_2$ in zero magnetic field at 1.6 K and its external magnetic field dependence. Furthermore, based on $^{59}$Co NMR data in both the paramagnetic and the incommensurate AFM states, we have determined the model-independent value of the AFM propagation vector k = (0, 0, 0.73 $pm$ 0.09)2$pi$/$c$ where $c$ is the $c$-axis lattice parameter. The temperature dependence of k is also discussed.
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