This paper deals with the aberrations of optical systems consisting of cylindrical components with their axes, parallal and having a common axis of symmetry. By symmetry and by a proper choice of the parameters for describing an optical ray, it is found that for primary aberrations the independent aberration terms amount to eight. For a. telescopic system the number of terms reduces to six. By method of vector analysis, it is further proved that the skew rays passing through such a systems is equivalent to a ray-tracing passing through its principal section but with the respective refractive index of each medium changed from n to (n2-η2)1/2, η being the direction cosine of the ray in the direction of cylindrical axes times n, an invariant throughout the system for a given ray. Thus the two term specifying "cylindrical" aberrations proper in a telescopic system (the other four terms being exactly the same as for spherical surfaces) can be treated in a similar way as longitudinal and transversal "chromatic" aberrations. However, the connection of such aberrations requires choice of optical materials difficult to comply with what is necessary for proper chromatic correction. On the otherhand, the serious effect of distortion usually found in cylindrical telescopic systems should be attributed as mainly intrinsic to Gaussian optics with which the practical requirement in imagery in such systems does not fully agree.