Alpha-morpholino subunits and polymer compositions composed of alpha-morpholino subunits are disclosed. These subunits can be linked together by uncharged linkages, one to three atoms in length, joining the morpholino nitrogen of one subunit to the 5' exocyclic carbon of an adjacent subunit. Each subunit contains a purine or pyrimidine base-pairing moiety effective to bind by hydrogen bonding to a specific base or base-pair in a target polynucleotide. The polymers of the instant invention can be used in place of standard RNA or DNA oligomers. For example, the target-specific polymers of the invention can be used in a variety of diagnostic assays for detection of RNA or DNA having a given target sequence. Further, the polymers of the invention also have potential use as therapeutic agents.