The present invention is related to a steel composition, a process for producing a steel product having said composition, and said steel product itself. According to the invention, a cold-rolled, possibly hot dip galvanized steel sheet is produced with thicknesses lower than 1 mm, and tensile strengths between 800 MPa and 1600 MPa, while the A80 elongation is between 5 and 17%, depending on the process parameters. The composition is such that these high strength levels may be obtained, while maintaining good formability and optimal coating quality after galvanising. The invention is equally related to a hot rolled product of the same composition, with higher thickness (typically about 2 mm) and excellent coating quality after galvanising.