Helixes on Clifford surfaces in a hyperbolic space H^3 of positive curvature are investigated. We formulate the following facts for a Clifford surface of every type in the space H^3. A curve on a Clifford surface of the space H^3 is a helix if and only if it is a loxodrome. If a helix ξ on a Clifford surface of the space H^3 contains opposite vertices of the coordinate rectangle of the basic coordinate network, then the helix ξ divides this coordinate rectangle into two parts of equal areas. The absolute points of the hyperbolic axis of a Clifford surface in the space H^3 are poles of each loxodrome on this surface.
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