Pioneering works on multimode fiber transmission [1,2], dated 40 years ago, predicted the existence of multimode solitons, providing conditions for the temporal trapping of the input optical modes to form a spatiotemporal soliton [3-5]. Only recently [6-8], multimode solitons were experimentally investigated in graded-index multimode fibers (GRIN), unveiling the complexity of a new, uncharted field. In our work, we experimentally and numerically investigated the propagation of ultrashort pulses over long distances of GRIN fiber. We discovered a new class of spatiotemporal solitons with surprising properties: basically single-mode, they cannot be described by the variational theory; their pulsewidth and energy are independent of the input pulse duration, and appear to depend only on the fiber dispersive parameters and, therefore, the wavelength. The new solitons are promising for the delivery of high-energy laser beams, for high-power spatiotemporal mode-locked multimode fiber lasers, and for high-bit rate multimode fiber networks.