The first son of Stephen Peabody Meacham and Dorothy Maria Ransom, Alonzo (as he was sometimes known) was part of a westward Mormon migration from New York to Illinois, where he married Nancy Eliza Martin on March 13, 1842. The following excerpt from a "History of Nebraska" was published while Alonzo was still alive:

"DR. STEPHEN A. MECHAM, P.O. Bennet, one of Nebraska's oldest and most respected citizens. He is a native of St. Lawrence County, N.Y., and was born August 6, 1815. His father, Stephen, was a farmer, and the subject spent his earlier days in tilling the soil. However, when comparatively young, he turned his attention to the study of medicine, under the tutorship of his grandfather, Dr. Thomas Mecham, a prominent herbal physician in his day. When eighteen years of age he commenced to practice, and continued in New York until twenty-eight years of age, when he came West, locating at Springfield, Ill., where he engaged in practice, and studied under Dr. Todd, father-in-law of Abraham Lincoln. After four years in Springfield, came to Iowa, which at that time was a howling wilderness, locating on Sugar Creek, Lee County, a short distance from Montrose. In 1846 he located in Scott County, Iowa, fifteen miles north of Davenport, where he continued with farming and practicing his profession. In 1850 crossed the State, locating where the city of Council Bluffs now stands. In connection with his brother Lafayette, he helped to build the first log house there, and engaged in the blacksmithing and butchering business. In 1851 he was one of the members who helped to survey and lay out the town site of Omaha. Resided in Bluffs until 1855, when he removed to De Soto, Neb., a small village a short distance north of Omaha. Here he engaged in milling, but, owing to the dam giving away, and the expense incurred in reconstructing it three times, it proved disastrous to him financially. In the spring of 1858, with his family in the wagon, he arrived on the site of his present home. On the middle branch of the Little Nemaha he and others had made a detour of the country, and they all had agreed to locate there; but owing to the unprepossessing appearance of the country, all but two backed out. The country at that time was very crude, and it was quite a curiosity to see a white man. As to the location he chose, it was well selected and showed good judgment. He would be frequently asked by the wayfaring traveler, in latter years, why he settled in such an isolated place, and his answer was, that he proposed to raise potatoes for the laborers that would build a railroad by his door. How well his prophecy has been verified is obvious. The Doctor was always a staunch friend to the red man, and received many testimonials from them in return. He had serious obstacles to contend with at that early day. He was obliged to do his milling at Coonville, upon Plum Creek, and to make his round trip it would take two weeks. He would have to build his bridges going, and frequently be obliged to rebuild them coming back, owing to wash-outs. He made some little money by gathering salt on Salt Creek and drawing it to Iowa with cattle, where he sold it. His claim consisted of 360 acres. Of this he hired fifty acres broken, at an expense of $5 per acre. As the country began to settle he was called on by those in need of medical attendance, and soon attained a lucrative practice. So far as can be ascertained he was the first practitioner in what comprises now Lincoln District. Much credit is due the Doctor for the live interest he took in showing the country to the new comers. His latchstring was always on the outside, and many of the first residents of the State remember his hospitality. The first school in that vicinity was secured through his instrumentality, he hiring the teacher at his own expense; and he has always been identified with the educational and religious sentiment of the community. Although the doctor is well advanced in years, he still retains his mental and physical facilities and bids to be yet for many years numbered among the pioneers of Nebraska. He continues to practice, but does not court patronage, as he thinks it is about time to retire. In 1840 he married Miss Nancy Martin, an estimable lady, who has been with him through all his struggles and triumphs. She, too, is still hale and hearty, and bears but few marks of the early days."

NOTE: The Dr. Todd who Stephen studied medicine under was most likely Mary Todd's uncle (not her father) Dr. John Todd, who practiced in Springfield from 1829 until his death in 1865.