The following explanation is from the United Church of God's Statement of Belief on "Divorce and Remarriage" (see www.ucg.org/papers):
"Only the following two reasons can (but do not necessarily have to) dissolve a marriage in which a believer is involved.
"porneia, or sexual immorality. This would include in the broader sense all cases of sexual deviancy, adultery being an example. The implication is habitual sexual misconduct, but is not limited to this.
"Not pleased to dwell. Paul explains in the book of 1 Corinthians that if an unbeliever is not pleased to dwell and departs that a Christian is not 'under bondage.' An individual may express his/her displeasure in a number of ways—habitual misconduct such as immorality (refers back to implications of porneia), criminality, addictive behaviors, abuse, desertion or willful failure to provide physical support (1 Timothy 5:8 1 Timothy 5:8But if any provide not for his own, and specially for those of his own house, he has denied the faith, and is worse than an infidel.
American King James Version×). In such cases it may be appropriate for the 'believer' to initiate the proceedings."