I will present results of analysis of solar decametric radio bursts with unusual internal structure. First I will consider type II bursts revealing fiber structure of their emission bands in the dynamic spectrum. This structure appears in those events where there is a coronal mass ejection traveling in the near-solar space ahead of the shock wave responsible for the burst. The second part of the talk will be devoted to the so-called type IIId bursts with echo-components. Time profiles of these bursts have several components. According to observations with the Ukrainian T-shape radiotelescope (UTR-2) the apparent source moves or jumps over the solar disk during observation of such profiles. Based on modeling results, which will be presented, I suggest that both types of bursts can be explained by strong regular refraction of radio waves on large-scale electron density gradients in the corona.