In a method for making paper having dry strength, wet strength, temporary wet strength, or combinations thereof, the step which comprises adding, as a strength aid, to the stock at any stage prior to forming a web, an effective amount of an aldehyde-containing polysaccharide derivative which has a structure selected from the group consisting of ##STR51## wherein Sacch--O-- represents a polysaccharide molecule;
- n is 1 to 3;
- R.sup.11 and R.sup.12 are independently an alkyl, aryl, aralkyl, or alkaryl group when n is 1, R.sup.11 or R.sup.12 is one of the groups when n is 2, or R.sup.11 and R.sup.12 are not present when n is 3;
- R.sup.13 is an alkyl group, optionally containing an ether linkage, or an aralkyl group;
- R.sup.14 and R.sup.15 individually are hydrogen or a methyl group;
- R.sup.16, R.sup.17, and R.sup.18 individually are an alkyl group;
- A, A', A" and A"' are independently a lower alkyl group or A and A' together form at least a 5-membered cyclic acetal;
- and Y is an anion.