The atomic level structure of the element fermium was investigated for the first time using a sample of 2.7x10(10) atoms of the isotope 255Fm with a half-life of 20.1 h. The atoms were evaporated from a filament and stored in the argon buffer gas of an optical cell. Atomic levels were sought by the method of resonance ionization spectroscopy using an excimer-dye-laser combination. Two atomic levels were found at wave numbers (25 099.8+/-0.2) and (25 111.8+/-0.2) cm(-1). Partial transition rates to the 5f(12)7s(2) (3)H(e)(6) ground state have been determined from their saturation characteristics. Multiconfiguration Dirac-Fock calculations suggest that the leading orders of these levels could be the 5f(12)7s7p (5)I(o)(6) and 5f(12)7s7p (5)G(o)(5) terms.