Quantitative trait loci analyses have revealed an important role for genetic variants in regulating alternative splicing (AS) and alternative cleavage and polyadenylation (APA) in humans. Yet, these studies are generally performed with mature mRNA, so they report on the outcome rather than the processes of RNA maturation and thus may overlook how variants directly modulate pre-mRNA processing. The order in which the many introns of a human gene are removed can substantially influence AS, while nascent RNA polyadenylation can affect RNA stability and decay. However, how splicing order and poly(A) tail length are regulated by genetic variation has never been explored. Here, we used direct RNA nanopore sequencing to investigate allele-specific pre-mRNA maturation in 12 human lymphoblastoid cell lines. We found frequent splicing order differences between alleles and uncovered significant single nucleotide polymorphism (SNP)-splicing order associations in 17 genes. This included SNPs located in or near splice sites as well as more distal intronic and exonic SNPs. Moreover, several genes showed allele-specific poly(A) tail lengths, many of which also had a skewed allelic abundance ratio. HLA class I transcripts, which encode proteins that play an essential role in antigen presentation, showed the most allele-specific splicing orders, which frequently co-occurred with allele-specific AS, APA or poly(A) tail length differences. Together, our results expose new layers of genetic regulation of pre-mRNA maturation and highlight the power of long-read RNA sequencing for allele-specific analyses.