Method for production of a cold- or hot-rolled steel strip made of an ultrastrong, air-hardenable multiphase steel with minimum tensile strengths in the longitudinal and transverse direction to the rolling direction before the air-hardening of 750 Mpa, having excellent processing properties consisting of the elements - contents in % by weight - C ≥ 0.075 to ≤ 0.115 Si ≥ 0.200 to ≤ 0.300 Mn ≥ 1.700 to ≤ 2.300 Cr ≥ 0.280 to ≤ 0.480 A1 ≥ 0.020 to ≤ 0.060 N ≥ 0.0020 to ≤ 0.0120 S ≤ 0.0050 Nb ≥ 0.005 to ≤ 0.050 Ti ≥ 0.005 to ≤ 0.050 B ≥ 0.0005 to ≤ 0.0060 Ca ≥ 0.0005 to ≤ 0.0060 Cu ≤ 0.050 Ni ≤ 0.050 remainder iron, including normal steel-accompanying, melting-produced impurities, in the case of which, with respect to as wide a process window as possible during the continuous annealing of hot- or cold strips made of this steel, the total content of Mn+Si+Cr dependent upon the strip thickness to be produced, is adjusted as follows: up to 1.00 mm: total of Mn+Si+Cr ≥ 2.350 and ≤ 2.500% by weight above 1.00 to 2.00 mm: total of Mn+Si+Cr > 2.500 ≤ 2.950% by weight above 2.00 mm: total of Mn+Si+Cr > 2.950 ≤ 3.250% by weight, and with strip thicknesses up to 1.00 mm, the Mn content is ≥ 1.700 to ≤ 2.000%, with strip thicknesses above 1.00 to 2.00 mm, the Mn content is ≥ 1.850 to ≤ 2.150%, with strip thicknesses above 2.00 mm, the Mn content is ≥ 2.000 to ≤ 2.300%, in which the required structure is produced during a continuous annealing, the cold- or hot-rolled steel strip being heated, during the continuous annealing, to a temperature in the range of 700 to 950°C and the annealed steel strip being cooled subsequently from the annealing temperature at a cooling rate between approx. 15 and 100°C / s to a first intermediate temperature of approx. 300 to 500°C, subsequently with a cooling rate between approx. 15 and 100°C / s to a second intermediate temperature of approx. 160 to 250°C, subsequently the steel strip being cooled at a cooling rate of approx. 2 to 30°C / s until reaching room temperature in air or the cooling being maintained with a cooling rate between approx. 15 and 100°C / s from the first intermediate temperature to room temperature. up to 1.00 mm: total of Mn+Si+Cr ≥ 2.350 and ≤ 2.500% by weight above 1.00 to 2.00 mm: total of Mn+Si+Cr > 2.500 ≤ 2.950% by weight above 2.00 mm: total of Mn+Si+Cr > 2.950 ≤ 3.250% by weight, and with strip thicknesses up to 1.00 mm, the Mn content is ≥ 1.700 to ≤ 2.000%, with strip thicknesses above 1.00 to 2.00 mm, the Mn content is ≥ 1.850 to ≤ 2.150%, with strip thicknesses above 2.00 mm, the Mn content is ≥ 2.000 to ≤ 2.300%, in which the required structure is produced during a continuous annealing, the cold- or hot-rolled steel strip being heated, during the continuous annealing, to a temperature in the range of 700 to 950°C and the annealed steel strip being cooled subsequently from the annealing temperature at a cooling rate between approx. 15 and 100°C / s to a first intermediate temperature of approx. 300 to 500°C, subsequently with a cooling rate between approx. 15 and 100°C / s to a second intermediate temperature of approx. 160 to 250°C, subsequently the steel strip being cooled at a cooling rate of approx. 2 to 30°C / s until reaching room temperature in air or the cooling being maintained with a cooling rate between approx. 15 and 100°C / s from the first intermediate temperature to room temperature.