Several models of partially observed diffusion processes with small diffusion coefficients of the same order in the state and observation equations are considered. These models are assumed to depend on some finite-dimensional unknown parameters, and the main problem is the construction of adaptive filters. These constructions are realized in several steps. First, by observations on a relatively small learning interval, the preliminary consistent estimators are proposed, then these estimarors are used for the construction of the One-step MLE-process. In the last step, the adaptive filter is obtained by the substitution of this estimator process in the equations of filtration. In the first section, the initial value is supposed to be known. In the second section, the initial values are estimated in different situations. Then the same program of adaptive filtering is realized in the third section for conditionally Gaussian systems. The nonlinear partially observed systems are studied in the fourth section. Using two approximations of these systems, some heuristic adaptive filters are proposed. In the last section, the partially observed linear system with different order small noises in the observation and state equations is studied. It is supposed that the system depends on some unknown parameters and the adaptive filters are costructed.