The objective of presented article is in application of methods of theory of oscillations in elaboration of new fish-type movers . Analysis of real fish swimming and robot fish mechanisms shows that as the first approximation plane motion of a robot fish model (hull, caudal fin and tail) may be described as a system with five degrees of freedom. To investigate efficiency of robot fish parts actuations, following simplifications were used: a) point between tail and hull is fixed and system has three degrees of freedom; b) hull is fixed and system has two degrees of freedom; c) point between tail and hull is fixed and caudal fin does not move relatively to tail. In such case system has two degrees of freedom. The last case is analyzed more in details, and differential equations of tail and hull motion are written for further use to investigate control mechanisms. In such differential equations we need to take into account direction of a rotation and action of resistance forces. Equations allow us to investigate different characteristics for robot fish, such as propulsion efficiency and rotation steering efficiency.