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<p/> <p>We deal with the nonhomogeneous A-harmonic equation <inline-formula> <graphic file="1029-242X-2010-520240-i1.gif"/></inline-formula> and the related conjugate A-harmonic equation <inline-formula> <graphic file="1029-242X-2010-520240-i2.gif"/></inline-formula>. Some priori estimates about solutions to these equations are obtained, which generalize some existing results. Particularly, we obtain the same estimate given by Theorem 1 of Iwaniec (1992) for the weak solution to the first equation under weaker conditions by a simpler method.</p>