Recently solar Type III bursts with fine time structure have been observed by radio telescope UTR-2 at frequencies 10 - 30 MHz. For the first time Type III-like bursts with high frequency drift rates were observed at these frequencies too. All this became possible due to both high sensitivity and high time resolution of UTR- 2. The properties of decameter Type III bursts can be understood if we take into account the spatial dependence of the electromagnetic wave group velocity as well as the fine spatial structure of the cloud of fast electrons responsible for Type III bursts. These effects are considered numerically in this paper. The fine time structure of Type III bursts is shown to be observed in the days when the associated active region is situated near the central meridian. In other days such structures disappeared. The Type III-like bursts with frequency drift rates of 10 - 20 MHz/s should also be observed, when the associated active region is near the central meridian. These peculiarities are confirmed by observations.