  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 curves analyses combining 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 possible 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 $\delta$ Sct type pulsator with a dominant
pulsation frequency of 18.58 d$^{-1}$ based on our $B$ filter residual light
curve although it can not be justified by 30-minute cadence TESS data. No
satisfactory evidence of pulsational behaviour for V1241 Tau was verified.
Finally, the evolutionary tracks of the components of both systems are
calculated, while their locations within evolutionary diagrams are compared
with other Algol-type systems.
