This paper is concerned with convergence analysis of general stochastic algorithms of the following form: \(\theta_n=\theta_{n-1}+ \gamma_n H(\theta_{n-1}, X_n)\), where \(\gamma_n\) is a nonnegative decreasing sequence, \(X_n\) is a ``somehow stationary'' sequence, and \(\theta_n\) is the estimates solution of \(E[H(\theta, X)]=0\). The author first rewrites the algorithm into \(\theta_n= \theta_{n-1}+ \gamma_n h(\theta_{n-1})+ \gamma_n\eta_n\), then gives conditions on the field \(h\) under which the condition that \(\theta_n\) does not tend to infinity will gurantee the convergence to some limit \(\theta^*\in \{h=0\}\) for deterministic \(\eta\). An asymptotic formula for the estimation error is also given which leads to the central limit theorem in stochastic settings. The results are extended to the case where a projection is introduced to establish stability. The approach is used to prove the convergence of a stochastic algorithm with Markovian settings. Application examples such as the construction of a blind equalizer and eigenvalue estimation are presented.