Dual-phase steels and a process for producing a family of dual-phase steels that have a low YS/TS ratio and tensile strength above 590 MPa. The process includes employing low annealing temperatures combined with specific cooling strategies using gas jet rapid cooling equipped with “Ultra Rapid Cooling” (URC) capacity in the cooling tower. The process can also include the production of dual-phase steels with tensile strengths of at least 690 MPa by processing steels with specific cooling strategies using the URC having a refined Mo content towards the higher end of the chemical composition range mentioned in the current stated invention.