An unsteady mixed convection flow over a permeable nonlinearly stretching vertical slender cylinder is considered to investigate the combined effects of thermal and mass diffusion in the presence of surface mass transfer and linear chemical reaction, where the slender cylinder is in line with the flow. The unsteadiness in the flow, temperature, and concentration fields is caused by the continuously nonlinearly stretching vertical slender cylinder. The effect of surface curvature is also taken into account, particularly for the applications of wire and fiber drawing where exact predictions are expected. The governing boundary layer equations are transformed into a nondimensional form by a group of nonsimilar transformations. The resulting system of coupled nonlinear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical computations are performed to understand the physical situations of linearly and nonlinearly stretching surface for various values of the governing parameters to display the effects of velocity, temperature, and concentration profiles graphically. Our main objective in this work is to focus on opposing flow situations. Numerical results for the local skin-friction coefficient, local Nusselt number, and local Sherwood number are also presented. The present results are compared with previously published work, and these comparisons are found to be in excellent agreement. © 2013 Copyright Taylor and Francis Group, LLC.