The relative merits of using sequential unconstrained methods for solving: minimizef(x) subject togi(x) ź 0, i = 1, ź, m, hj(x) = 0, j = 1, ź, p versus methods which handle the constraints directly are explored. Nonlinearly constrained problems are emphasized. Both classes of methods are analyzed as to parameter selection requirements, convergence to first and second-order Kuhn-Tucker Points, rate of convergence, matrix conditioning problems and computations required.