With another round of state budget cuts looming, Margaret H. Marshall, chief justice of the Supreme Judicial Court of Massachusetts, warned yesterday that financial troubles are clogging the courts, pulling probate officers from Boston schools, and decimating the ranks of court-appointed guardians.

Problems could range from long delays for hearings to get protective orders in family court to less court oversight of troubled youth to routine business taking months rather than weeks as courthouses are forced to eliminate workers.

“In my judgment, justice is in jeopardy in Massachusetts,’’ she said at her annual address to the legal community in downtown Boston. “These are strong words, and I use them with care.’’

For the first time in Marshall’s decade as chief justice, she focused her talk on a single topic and struck an unusually foreboding and political tone.