The signal properties of radio frequency (rf) (SQUIDs) based on YBa2Cu3O7−x symmetrical 30° and asymmetrical 45° grain-boundary Josephson junctions have been experimentally investigated. Both amplitude as well as phase detection have been used to read out the SQUID output signal. Comparison of the SQUID output signals to each other is given. It is shown that peculiarities of the rf SQUID response of SQUIDs with a 45° grain-boundary Josephson junction are consistent with an unconventional current-phase relation (CPR) of the Josephson junction, namely, the CPR contains a finite amplitude of the second harmonic.