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We report on the energy-resolved timing and phase-resolved spectral analysisof X-ray emission from PSR J0659+1414 observed with XMM-Newton and NuSTAR. Wefind that the new data rule out the previously suggested model of thephase-dependent spectrum as a three-component (2 blackbodies + power-law)continuum, which shows large residuals between $0.3-0.7$ keV. Fitting neutronstar atmosphere models or several blackbodies to the spectrum does not providea better description of the spectrum, and requires spectral model componentswith unrealistically large emission region sizes. The fits improvesignificantly if we add a phase-dependent absorption feature with centralenergy $0.5-0.6$ keV and equivalent width up to $\approx 50$ eV. We detectedthe feature for about half of the pulse cycle. Energy-resolved pulse profilessupport the description of the spectrum with a three-component continuum and anabsorption component. The absorption feature could be interpreted as anelectron cyclotron line originating in the pulsar magnetosphere and broadenedby the non-uniformity of the magnetic field along the line of sight. Thesignificant phase-variability in the thermal emission from the entire stellarsurface may indicate multi-polar magnetic fields and a non-uniform temperaturedistribution. The strongly pulsed non-thermal spectral component detected withNuSTAR in the $3-20$ keV range is well fit by a power-law model with a photonindex $\Gamma=1.5\pm0.2$.

Possible phase-dependent absorption feature in the x-ray spectrum of the middle-aged PSR J0659+1414