  We theoretically investigate asymmetric two-junction SQUIDs with different
current-phase relations in the two Josephson junctions, involving higher
Josephson harmonics. Our main focus is on the "minimal model" with one junction
in the SQUID loop possessing the sinusoidal current-phase relation and the
other one featuring additional second harmonic. The current-voltage
characteristic (CVC) turns out to be asymmetric, $I(-V) \neq -I(V)$. The
asymmetry is due to the presence of the second harmonic and depends on the
magnetic flux through the interferometer loop, vanishing only at special values
of the flux such as integer or half-integer in the units of the flux quantum.
The system thus demonstrates the flux-tunable Josephson diode effect (JDE), the
simplest manifestations of which is the direction dependence of the critical
current. We analyze asymmetry of the overall $I(V)$ shape both in the absence
and in the presence of external ac irradiation. In the voltage-source case of
external signal, the CVC demonstrates the Shapiro spikes. The integer spikes
are asymmetric (manifestation of the JDE) while the half-integer spikes remain
symmetric. In the current-source case, the CVC demonstrates the Shapiro steps.
The JDE manifests itself in asymmetry of the overall CVC shape, including
integer and half-integer steps.
