Abstract: In this paper we shall consider the cases where the zeroes or extreme points of regression function h(x) are not singal, the measurement errors are quite general. When it is known a priori that the zero set or extreme set of h(x) lie in some bounded close set, a truncated Bobbins-Monro (RM) or Kiefer-Wolfowitz (KW) algorithms is suggested, and the strong convergence of the algorithms is proved under simple conditions. For the same measurement errors to search zero set of linear fuction or extreme set of quadratic function usual RM or KW procedures can guarantee their strong convergence under rather simple conditions.