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The predominant d-wave pairing symmetry in high temperature superconductors leads to an unconventional current - phase relation in Josephson junctions. This circumstance may induce new effects in the dynamics of dc SQUIDs. In this contribution we report on the measurements of the dependence of the SQUID Josephson current on the external magnetic field taken at very low temperatures, down to 20 mK. Different grain boundaries have been fabricated by using the biepitaxial and the bicrystal technique. Some of the effects which are induced by a nonsinusoidal current - phase relation can be clearly identified in the dynamics of the SQUIDs. The experimental data are also compared with theoretical simulations taking into account the inductance of the loop. The data show that, in specific conditions, a non-negligible inductance of the loop can induce effects similar to an unconventional current - phase relation, with a pronounced second harmonic sin( 2 phi) term. This fact has to be taken into account when designing d- wave SQUIDs for quantum circuitry.