A flat steel product having a tensile strength of at least 1200 MPa and consists of steel containing (wt %) C: 0.10-0.50%, Si: 0.1-2.5%, Mn: 1.0-3.5%, Al: up to 2.5%, P: up to 0.020%, S: up to 0.003%, N: up to 0.02%, and optionally one or more of the elements “Cr, Mo, V, Ti, Nb, B and Ca” in the quantities: Cr: 0.1-0.5%, Mo: 0.1-0.3%, V: 0.01-0.1%, Ti: 0.001-0.15%, Nb: 0.02-0.05%, wherein Σ(V, Ti, Nb)≦0.2% for the sum of the quantities of V, Ti and Nb, B: 0.0005-0.005%, and Ca: up to 0.01% in addition to Fe and unavoidable impurities. The flat steel product has a microstructure with (in surface percent) less than 5% ferrite, less than 10% bainite, 5-70% untempered martensite, 5-30% residual austenite, and 25-80% tempered martensite, at least 99% of the iron carbide contained in the tempered martensite having a size of less than 500 nm.