SW Cyg and DD Dra are two Algol-type eclipsing binary systems. Both contain an A2-type main-sequence primary and a K0-type secondary component with a rather deep primary light minimum in their light curves (2.m6 and 3.m 8, respectively). In the present paper, orbital period changes of these stars are studied based on the analyses of their century-long times of light minimum. Several period jumps are found to superimpose on a rapid secular increase (dP/dt = +4.71 × 10-6 and +4.24 × 10-6 days/year, respectively). Since the period increases are rather rapid, the mass exchange between the components would be dynamical. SW Cyg is a low-mass ratio system (q = 0.20) and it is expected that the mass ratio of RR Dra may also be very low because of the rather deep primary eclipse minimum. The rapid period increases suggest that a rapid mass transfer also occurs in a low-mass ratio Alogl-type close binary which is opposite to the theoretically evolutionary scheme of the binary star. The period jumps superimposed on the long-term increases are caused by the structura variation of the cool mass-loser via instabilities in the convective outer layer (COL) or via cyclic magnetic activity of the K0-type components. As the period jumps do not occur in a short-term alternating way, the structura change caused by instabilities in the COL via a dynamical mass loss from the cool subgiant may be more plausible.