The orbital period changes of two low-mass-ratio and deep-contact binaries, FN Cam and KN Per, are investigated by using all available times of light minimum taken from the databases and literature. It is found that the orbital periods of FN Cam and KN Per show secular increase at a rate of P˙ = 4.38 ×10-7 days year-1 and P˙ = 4.18 ×10-7 days year-1 , respectively. The secular period increase suggests that FN Cam and KN Per are undergoing continuous mass transfer from the less massive secondary component to the more massive primary one. A statistical analysis of 53 low-mass-ratio and deep-contact binaries indicates that all of them should contain at least a continuous period change (secular increase/decrease or cyclic oscillation). Moreover, the rates of the secular period variations can be at a common level of P˙ ∼10-7 days year-1. In addition, the cyclic period oscillation has been detected for only 43% of sample stars, which indicates that it should be not popular for all low-mass-ratio and deep-contact binaries.