We present new photometric and spectroscopic observations and analyses for the eclipsing binary systems V1241 Tau and GQ Dra. Our photometric light and radial velocity curve analyses combined with the TESS light curves show that both are conventional semi-detached binary systems. Their absolute parameters are also derived. We present the O-C analyses of the systems and we propose the most likely orbital period modulating mechanisms. Furthermore, Fourier analyses are applied to the photometric residual data of the systems to check for the pulsational behavior of the components. We conclude that the primary component of the system GQ Dra is a delta Set type pulsator with a dominant pulsation frequency of 18.58 d(-1) based on our B filter residual light curve although it cannot be verified by 30-minute cadence TESS data. No satisfactory evidence of pulsational behavior for V1241 Tau was verified. Finally, the evolutionary tracks of the components of both systems are calculated. Their locations within evolutionary diagrams are compared with other Algol-type systems.