The slow combustion of the simplest hydrocarbons in a "wall-less" reactor with laser heating has been studied. In such a reactor, combustion proceeds in the laser beam, while the reactor's wall is at room temperature and does not take part in the process. It has been shown that conversion of propane plus oxygen mixtures can be observed at temperatures above 800 K. Ethylene, propylene, methane, and hydrogen were found to be the major products, indicating the dominant role of the cracking route in this process. At the same time oxygen was not consumed and oxygenated products were detected only in trace concentrations. However, in the absence of oxygen the cracking process does not proceed. Chain initiation in a "wall-less" reactor occurs homogeneously, while, in conventional heated reactors chain initiation is provided at lower temperatures (600-650 K) by heterogeneous reactions on the reactor's wall. It has been established that the reversible reaction forming alkyl peroxy radicals in R + O2 = RO2 is of great importance in the competition between oxidative and cracking routes. In a "wall-less" reactor when a sufficient rate of chain initiation can be reached at temperatures above 800 K, this equilibrium is shifted to form alkyl radicals. Reactions of these radicals become dominant and hydrocarbon conversion leads to products from cracking. The conversion of methane plus oxygen mixtures starts at temperatures 1000 K and proceeds via the oxidative route, because methyl radicals, unlike propyl radicals, do not decay, but react with oxygen in different ways. The results reveal the role of heterogeneous factors in the chemistry of slow combustion and show ways to carry out these processes with a high selectivity.