We have carried out muon spin relaxation (μSR), neutron diffraction, and inelastic neutron scattering (INS) investigations on polycrystalline samples of Ce(Ru1−xFex)2Al10 (x=0, 0.3, 0.5, 0.8, and 1) to investigate the nature of the ground state (magnetic ordered versus paramagnetic) and the origin of the spin-gap formation as evident from the bulk measurements in the end members. Our zero-field μSR spectra clearly reveal coherent two-frequency oscillations at low temperature in x=0, 0.3, and 0.5 samples, which confirm the long-range magnetic ordering of the Ce moment with Nèel temperature TN=27, 26, and 21 K, respectively. On the other hand, the μSR spectra of x=0.8 and x=1 down to 1.4 K and 0.045 K, respectively, exhibit a temperature-independent Kubo-Toyabe term, confirming a paramagnetic ground state. The long-range magnetic ordering in x=0.5 below 21 K has been confirmed through the neutron diffraction study. INS measurements of x=0 clearly reveal the presence of a sharp inelastic excitation near 8 meV between 5 K and 26 K, due to an opening of a gap in the spin excitation spectrum, which transforms into a broad response at and above 30 K. Interestingly, at 4.5 K, the spin-gap excitation broadens in x=0.3 and exhibits two clear peaks at 8.4(3) and 12.0(5) meV in x=0.5. In the x=0.8 sample, which remains paramagnetic down to 1.2 K, there is a clear signature of a spin gap of 10–12 meV at 7 K, with a strong wave-vector–dependent intensity. Evidence of a spin gap of 12.5(5) meV has also been found in x=1. The observation of a spin gap in the paramagnetic samples (x=0.8 and 1) is an interesting finding in this study, and it challenges our understanding of the origin of the semiconducting gap in CeT2Al10 (T = Ru and Os) compounds in terms of a hybridization gap opening only a small part of the Fermi surface, gapped spin waves, or a spin-dimer gap.