Transient, spherically symmetric, combustion of single and multi-component liquid n-alkane droplets is numerically simulated with a model that includes gas phase detailed, multi-component molecular transport and complex chemical kinetics. A compact semi-detailed kinetic mechanism for n-heptane and n-hexadecane oxidation consisting of 51 species (including He, Ar, and N-2) and 282 reactions is used to describe the gas phase. Non-luminous, gas phase radiative heat transfer and conservation of energy and species within the liquid droplet interior are also considered. Computed quasi-steady flame structure for pure n-heptane droplets is compared with that produced using the kinetic mechanism of Warnatz (frequently used in the past for modeling both premixed and diffusion flame properties). Transient calculations are also compared with the numerical results of King, which consider infinite rate chemical kinetics, but temperature dependent molecular diffusion. Modeling results are in reasonable agreement with small-diameter, drop tower experiments, though slew convective effects and droplet sooting effects exist in the experimental data. Comparisons with isolated large-diameter free droplet data (1 atm, He/O-2 mixtures and air) from recent space experiments are reasonable for droplet gasification rate, flame position, and flame extinction. Very small extinction diameters are predicted for small initial diameter droplets (<1 mm). As droplet size is increased, or oxygen index is decreased, the model predicts decreasing gasification rates and for an appropriate range of parameters, radiative flame extinction. Bi-component droplet combustion of n-heptane and n-hexadecane is also considered. Modeling results qualitatively reproduce experimentally observed, multi-stage burning, resulting from the volatility differential and diffusional resistance of the liquid components. Internal liquid convection effects are examined by parametrically varying an effective liquid mass diffusivity. Flame extinction can occur either in the initial or the secondary droplet heating period, with subsequent, continuing vaporization of the more volatile component from the residual heat within the liquid phase.