A method for producing a high-strength cold rolled steel sheet or strip is disclosed. Steel comprising0.05 to 0.15% of C;0.02 to 0.30% of Si;0.10 to 1.5% of Mn;0.02 to 0.07% of Al; andA total of 0.02 to 0.15% of at least one ofNb, V, Ti and Zr;With the remainder being iron and unavoidable impurities,Is hot rolled whereafter the hot rolled steel sheet or strip is coiled at a temperature of not more than 750.degree.C. The coiled sheet or strip is then cold rolled whereafter the cold rolled steel sheet or strip is subjected to annealing at a temperature between 670.degree.C and 900.degree.C for 20 seconds to 10 minutes.