We here investigate drawing of multi-layered Newtonian and non-Newtonian fluid fibers, drawn under isothermal and non-isothermal conditions. We first develop one-dimensional equations governing mass, momentum, and energy balances and solve them numerically to obtain steady state draw root shape, velocity, and temperature profiles. These solutions are then used to perform linear stability analysis. For the case of isothermal draw, the system displays an oscillatory instability when the draw ratio (ratio of cross-sectional areas of fiber at the entrance and exit of the drawing) is higher than a critical draw ratio (highest stable draw ratio) of about 20.21. Investigation of stability behavior under non-isothermal draw conditions is performed by considering radiative heating and convective cooling. Employing only radiative heating enhances the critical draw ratio, and simultaneous heating and convective cooling increase the critical draw ratio even further. For the case of simultaneous heating and cooling, with increasing convective cooling strength, the critical draw ratio first increases, reaches a maximum, and then gradually decreases. However, with only convective cooling, the critical draw ratio decreases with an increase in convective cooling strength. We also find that the stabilizing effect of a non-isothermal operation can be enhanced by considering fluids with higher viscosity sensitivity to temperature, increasing the maximum temperature, and for sharper attenuation of the fiber cross-sectional area with length. For the case of isothermal drawing of non-Newtonian fluid fibers, the system has a higher critical draw ratio for shear thickening fluids (power-law exponent, n > 1). In contrast, the use of a shear thinning fluid (n < 1) reduces the critical draw ratio. Consideration of a non-isothermal operation of non-Newtonian fluid fibers reveals that the critical draw ratio is primarily determined by the non-Newtonian behavior rather than the non-isothermal drawing. (C) 2010 Elsevier Ltd. All rights reserved.