Method for producing a hot-dip coated, high-strength, flat steel product, having the following steps: - Providing a flat steel product having the following chemical composition in mass %: C: 0.04 to 0.40, advantageously, 0.04 to 0.30, particularly advantageously 0.08 to 0.23 Mn: 0.8 to 3.0, advantageously 1.0 to 2.5 Si: ≤ 2.0, advantageously ≤ 1.8, particularly advantageously ≤ 1.5, in particular ≤ 0.7 Al: 0.01 to 2.0, advantageously up to 0.8, particularly advantageously up to 0.4 P ≤ 0.1, S ≤ 0.005, N ≤ 0.02, and, optionally, one or more of the following elements: Cr: 0.1 to 0.9, advantageously 0.2 to 0.7 B: 0.001 to 0.008 Ti: 0.01 to 0.1 V: 0.01 to 0.2 Nb: 0.01 to 0.1, advantageously 0.02 to 0.06 Mo: 0.05 to 0.5, advantageously 0.1 to 0.25 Ni: 0.15 to 0.5 Cu: 0.15 to 0.2 remainder iron and unavoidable impurities, - cleaning the surface of the flat steel product - applying an iron-based layer to the surface of the flat steel product as pre-coating with an average thickness of between 0.1 μm and 1.2 μm, wherein the iron-based coating after the coating and before the annealing treatment contains oxygen - annealing in an iron-reducing furnace atmosphere at temperatures above 700 °C, wherein the decadic logarithm from the ratio of hydrogen partial pressure and water partial pressure in the furnace atmosphere corresponds to the following formula: 0.35 + 0.053 x ≤ lg p H 2 p H 2 O ≤ 3.1 + 0.09 x where x = oxygen content in the iron-based coating in mass % after deposition and before the annealing treatment p H2 = hydrogen partial pressure in bar p H2O = water partial pressure in bar. - hot-dip coating the thus treated and annealed flat steel product with a zinc-based melt containing substantially 0.5 to 8.0 mass % magnesium and 0.5 to 8.0 mass % aluminium, less than 1 mass % iron, and unavoidable impurities. - Providing a flat steel product having the following chemical composition in mass %: C: 0.04 to 0.40, advantageously, 0.04 to 0.30, particularly advantageously 0.08 to 0.23 Mn: 0.8 to 3.0, advantageously 1.0 to 2.5 Si: ≤ 2.0, advantageously ≤ 1.8, particularly advantageously ≤ 1.5, in particular ≤ 0.7 Al: 0.01 to 2.0, advantageously up to 0.8, particularly advantageously up to 0.4 P ≤ 0.1, S ≤ 0.005, N ≤ 0.02, and, optionally, one or more of the following elements: Cr: 0.1 to 0.9, advantageously 0.2 to 0.7 B: 0.001 to 0.008 Ti: 0.01 to 0.1 V: 0.01 to 0.2 Nb: 0.01 to 0.1, advantageously 0.02 to 0.06 Mo: 0.05 to 0.5, advantageously 0.1 to 0.25 Ni: 0.15 to 0.5 Cu: 0.15 to 0.2 remainder iron and unavoidable impurities, C: 0.04 to 0.40, advantageously, 0.04 to 0.30, particularly advantageously 0.08 to 0.23 Mn: 0.8 to 3.0, advantageously 1.0 to 2.5 Si: ≤ 2.0, advantageously ≤ 1.8, particularly advantageously ≤ 1.5, in particular ≤ 0.7 Al: 0.01 to 2.0, advantageously up to 0.8, particularly advantageously up to 0.4 P ≤ 0.1, S ≤ 0.005, N ≤ 0.02, and, optionally, one or more of the following elements: Cr: 0.1 to 0.9, advantageously 0.2 to 0.7 B: 0.001 to 0.008 Ti: 0.01 to 0.1 V: 0.01 to 0.2 Nb: 0.01 to 0.1, advantageously 0.02 to 0.06 Mo: 0.05 to 0.5, advantageously 0.1 to 0.25 Ni: 0.15 to 0.5 Cu: 0.15 to 0.2 remainder iron and unavoidable impurities, Cr: 0.1 to 0.9, advantageously 0.2 to 0.7 B: 0.001 to 0.008 Ti: 0.01 to 0.1 V: 0.01 to 0.2 Nb: 0.01 to 0.1, advantageously 0.02 to 0.06 Mo: 0.05 to 0.5, advantageously 0.1 to 0.25 Ni: 0.15 to 0.5 Cu: 0.15 to 0.2 remainder iron and unavoidable impurities, - cleaning the surface of the flat steel product - applying an iron-based layer to the surface of the flat steel product as pre-coating with an average thickness of between 0.1 μm and 1.2 μm, wherein the iron-based coating after the coating and before the annealing treatment contains oxygen - annealing in an iron-reducing furnace atmosphere at temperatures above 700 °C, wherein the decadic logarithm from the ratio of hydrogen partial pressure and water partial pressure in the furnace atmosphere corresponds to the following formula: 0.35 + 0.053 x ≤ lg p H 2 p H 2 O ≤ 3.1 + 0.09 x where x = oxygen content in the iron-based coating in mass % after deposition and before the annealing treatment p H2 = hydrogen partial pressure in bar p H2O = water partial pressure in bar. x = oxygen content in the iron-based coating in mass % after deposition and before the annealing treatment p H2 = hydrogen partial pressure in bar p H2O = water partial pressure in bar. - hot-dip coating the thus treated and annealed flat steel product with a zinc-based melt containing substantially 0.5 to 8.0 mass % magnesium and 0.5 to 8.0 mass % aluminium, less than 1 mass % iron, and unavoidable impurities.