We report the experimental generation of two-soliton molecules in an all-polarization-maintaining ytterbium-doped fiber laser operating in the normal dispersion regime. These molecules exhibit an independently evolving phase and are characterized by a regular spectral modulation pattern with a modulation depth of 80% measured as an averaged value. Moreover, the numerical modeling confirms that the limited modulation depth of the spectrum is caused by the evolution of the phase difference between the pulses. © 2010 Optical Society of America.