A formulation for the noblinear analysis of two-dimensional steel frames under fire conditions using the finite element method is presented. Deterioration in material strength with increasing temperature is represented by a set of nonlinear stress-strain-temperature relationships using a Ramberg-Osgood equation in which creep effects are implicitly included. Structures subject to increasing loads or temperatures are analysed using an incremental Newton - Raphson iterative procedure. The analysis permits deformation history and either collapse load or critical temperature to be calculated at a specified temperature or load level respectively. It includes the effects of geometric nonlinearity, temperature dependent nonlinear material behaviour and variations in temperature distributions both along and across each member. The effects of thermal strains, residual stresses and thermal bowing are also considered and different material models may be used. Comparisons are made with fire test results on frames and columns that represent a wide range of problem parameters such as slenderness, end conditions, load levels and temperature distributions. In all cases, the agreement is very satisfactory. An example two-bay frame is analysed to illustrate the potential of the analysis and to show the influence of various forms of partial protection on the collapse temperature of sway frames.