Context : Aims : We report the identification of cyclical changes in the orbital period of the eclipsing cataclysmic variable HT Cas . Methods : We measured new white dwarf mid-eclipse timings and combined with published measurements to construct an observed-minus-calculated diagram covering 29 years of observations . Results : The data present cyclical variations that can be fitted by a linear plus sinusoidal function with period 36 yr and semi-amplitude \sim 40 s. The statistical significance of this period by an F-test is larger than 99.9 per cent . Conclusions : We combine our results with those in the literature to revisit the issue of cyclical period changes in cataclysmic variables and their interpretation in terms of a solar-type magnetic activity cycle in the secondary star . A diagram of fractional period change ( \Delta P / P ) versus the angular velocity of the active star ( \Omega ) for cataclysmic variables , RS CVn , W UMa and Algols reveal that close binaries with periods above the gap ( secondaries with convective envelopes ) satisfy a relationship \Delta P / P \propto \Omega ^ { -0.7 \pm 0.1 } . Cataclysmic variables below the period gap ( with fully convective secondaries ) deviate from this relationship by more than 3- \sigma , with average fractional period changes \simeq 5 times smaller than those of the systems above the gap .