In the last decades, a great number of high resolution schemes (HRSs) have been proposed to obtain highly accurate and non-oscillatory solutions in the numerical simulation of the flows. In this work, the performance of various HRSs for time-dependent problems is studied. To do this, HRSs are applied to a test problem. In the test problem, advection of rectangular, semi-ellipse, sine-squared and triangular profiles in a constant velocity field is solved. Numerical solutions are obtained for each profile for CFL numbers of 0.98, 0.50, 0.25, 0.10 and 0.05 and for non-dimensional times of 50, 100 and 250. Computations show that some HRSs are not bounded. Also, It is observed that compressive schemes have less error than diffusive schemes and give more satisfactory results particularly for small CFL numbers for time-dependent problems.