In this paper a number of scanning algorithms for construction of basins of attraction of periodic regimes of nonlinear oscillatory systems with single degree of freedom is described. Algorithms are based on an exhaustive search of initial conditions in the given area of the phase plane and on the further analysis of the stationary motions. It should be noted that basins of attraction usually contain large homogeneous parts, belonging to the same region, whose continuous scanning does not give any useful information. This fact is taken into account here and the proposed algorithms are fulfilling the selective scanning near the boundaries of the basins, thereby forming the desired lines. As a result, the most of homogeneous regions are not tested and the number of examined starting points is significantly reduced. Here two groups of such algorithms are proposed. In the first group they are produced by repeated scanning with decreasing lead and excluding homogeneity of fragments. In the second one, the preliminary scan along the line limiting the search area is carried out and the end points of the boundaries of attraction domains are discovered. After this the selective scanning of these points is fulfilled and the demanded curves are detected gradually. These algorithms have been implemented and tested, and their comparative analysis on the example of the Duffing equation was conducted. The average time for selecting of the next initial point, the total number of points, which were used forconstruction and the accuracy of the obtained results were taken as the comparison criteria.