We have studied the magnetism in superconducting single crystals of EuFe2 As1.4 P0.6 by using the local probe techniques of zero-field muon spin rotation/relaxation and 151 Eu/57 Fe Mossbauer spec- troscopy. All of these measurements reveal magnetic hyperfine fields below the magnetic ordering temperature TM = 18 K of the Eu2+ moments. The analysis of the data shows that there is a coexistence of ferromagnetism, resulting from Eu2+ moments ordered along the crystallographic c-axis, and superconductivity below TSC approx 15 K. We find indications for a change in the dynamics of the small Fe magnetic moments (sim 0.07 mu B) at the onset of superconductivity: below TSC the Fe magnetic moments seem to be frozen within the ab-plane.