  We study the dynamical stability of Bose-Einstein condensates in an optical
lattice with a time-periodic modulation potential and a constant acceleration
force simultaneously. We derive the explicit expressions of quasienergies and
obtain the stability diagrams in the parameter space of the interaction
strength and the modulation amplitude. The ratio of the acceleration force to
the modulation frequency characterizes two cases: integer and non-integer
resonances. For integer resonances, the critical interaction strength
$g_{\mathrm{c}}$ shows an alternate behavior where the completely unstable
regions correspond to the negative effective tunneling strength. Among
non-integer resonances, we observe that $g_{\mathrm{c}}$ peaks are centered
around half-integer resonances for which the completely unstable regions
disappear, accompanied with a whole displacement of $g_{\mathrm{c}}$. Compared
with integer and half-integer resonances, the crossovers between them show no
explicit dependence of $g_{\mathrm{c}}$ on the modulation amplitude.
