We address the problem of monitoring a linear functional (c,x)E of an unknown vector x of a Hilbert space E, the available data being the observation z, in a Hilbert space F, of a vector Ax depending linearly on x through some known operator A is-an-element-of L(E; F). When E = E1 x E2, c = (c1, 0), and A is injective and defined through the solution of a partial differential equation, Lions ([6]-[8]) introduced sentinels s is-an-element-of F such that (s, Ax)F is sensitive to x1 is-an-element-of E1 but insensitive to x2 is-an-element-of E2. In this paper we prove the existence, in the general case, of (i) a generalized sentinel (s, sigma) is-an-element-of F x E, where F superset-of F with F dense in F, such that for any a priori guess x0 of x, we have FF’ + (sigma, x0)E = (c, x)E, where x is the least-square estimate of x closest to x0, and (ii) a family of regularized sentinels (s(n), sigma(n)) is-an-element-of F x E which converge to (s, sigma). Generalized sentinels unify the least-squares approach (by construction!) and the sentinel approach (when A is injective), and provide a general framework for the construction of "sentinels with special sensitivity" in the sense of Lions [8]).