Microgravity experiments have shown that near limit opposed flow flame-spread show unsteady oscillatory behavior marked with formation of flamelets. Here in this work an elaborate 3D numerical model is used to predict this near limit fame-spread behavior of a self-propagating flame over thin solid in microgravity. As the oxygen level is reduced steady, below certain value, flame-spread over wide thin solid fuel becomes unsteady. Two kinds of unsteady flame-spread phenomena were noted. In one a single flame oscillated back and forth near the fuel side edge and in other the multiple flamelets were formed which oscillated laterally. The former occurs at relatively higher oxygen levels and leads to formation of the later at still lower oxygen levels just ahead of extinction. It is noted that as oxygen level is reduced the amplitude of longitudinal oscillation increases leading to the splitting of flame which then exhibits lateral motion. The lateral oscillatory behavior spans over a wider range of oxygen level than that of longitudinal oscillatory flame behavior. The range of oxygen level over which the lateral oscillatory behavior is observed, increases with increase in fuel thickness and fuel width. The number of flamelets formed increases with increase in fuel width with typical flamelet size of 2-4 cm. Some of the flame behavior noted here are remarkably similar to those seen in the short duration drop tower test where heat loss from the flame was artificially enhanced. However, the numerical computations show that such oscillatory flames can exist for considerably long durations. © 2016 The Combustion Institute. Published by Elsevier Inc.