Over 11,000 second meiotic metaphase spreads stained for the pericentromeric region have been studied quantitatively in male mice of 14 strains. The sex-chromosome constitution of a cell could be judged objectively if X and Y chromosomes and ploidy were all scored. A bias arose if only Y chromosomes and ploidy were scored but could be corrected statistically. There was no sign of other forms of bias. The original contiguity of X and Y second metaphases in vivo was very occasionally evident in the preparations. Most of the subhaploid aneuploid counts were assumed to be artifactual. The incidence of truly aneuploid second metaphases in 13 strains was estimated as 0.38+/-0.12%. The estimated average rate per chromosome was 0.019+/-0.006%, with a comparable order of magnitude for the sex chromosomes alone. Simultaneous aneuploidy of two or more chromosomes of the haploid set was estimated to be very rare. Of the spreads from 13 strains, 9.6% were polyploid (2N, 3N, 4N) and showed most of the possible combinations of sex chromosomes. Nearly all the polyploid spreads were considered to arise by artifactual cell fusion at the time of second metaphase during the preparative technique, especially of the X and Y daughter-cell products of the first meiotic division. Other modes of origin (true polyploidy, accidental superposition of cells during preparation) were unlikely. The data could be accommodated by a statistical model with only four parameters. It allowed for artifactual fusion mainly between daughter cells but also between non-daughter cells, bias in one scoring method, and bias in the numbers of cells with given ploidy successfully mounted. Current techniques of chromosome preparation were thought to be wholly unsuitable for the recognition of true polyploidy. The artifactual origin of polyploid spreads was borne out by an absence of polyploid spermatozoa in 14 strains. There appeared to be a virtually constant transmission rate of paternal X and Y chromosomes from early meiosis to late blastocyst. The estimated rate of 49.05+/-0.67% with a Y chromosome also estimated the primary sex ratio. There was evidence of polymorphism in autosomal pericentromeric staining in 3 strains. No measure of the numbers of autosomes or sex chromosomes varied significantly between duplicate preparations or between duplicate males of a strain.