This paper describes the concept and preliminary investigations related to the development of simple bioinspired actuation mechanisms for the eyeballs of an android robotic face. Two design solutions for a one-degree-of-freedom mechanism are proposed and analytically studied according to linear models. Both of them are based on new contractile actuators made of electroactive polymers, employed as pseudomuscular devices. The actuators consist of dielectric elastomers and are capable of electrically driven linear contractions. The arrangement and the functionality of the actuators were conceived to mimic those of rectus-type human ocular muscles. Both the presented solutions rely on a couple of agonist-antagonist actuators, in order to enable bidirectional rotations of the eyeball around an axis. The two configurations basically differ in the presence/absence of pulleys, guiding tendon-like wires which connect the actuators to the eyeball. The influence on the system performances of both rest length and elastic modulus of the actuators was studied for both configurations. Geometrical constraints allow the configuration with pulleys to perform more than the other, despite a potential intrinsic superior efficacy of the latter. The paper describes also the assembly of a simple prototype version of the system and presents the results of preliminary tests. These permitted us to assess the feasibility of the proposed concept and suggested possible improvements.