The present invention relates to a novel pyrazolo[1,5-a]pyrimidine compound of the formula [I]: ##STR00001## wherein R.sup.1 and R.sup.2 are the same or different and an optionally substituted aryl group etc. Q is single bond, a methylene group or a group of the formula: --N(R.sup.Q)--, R.sup.Q is an alkyl group, Ring A is a substituted pyrazole ring fused to the adjacent pyrimidine ring having the following formula (A), (B) or (C), ##STR00002## R.sup.3 and R.sup.4 are the same or different and a hydrogen atom, a cyano group etc. E is one of the following groups (i) to (v): ##STR00003## R.sup.00 is an alkyl group, Q.sup.1 is a single bond etc., Q.sup.2 is a single bond or an alkylene group, one of R.sup.5 and R.sup.6 is a hydrogen atom or an alkyl group and the other is an alkyl group etc., one of R.sup.50 and R.sup.60 is a hydrogen atom or an alkyl group and the other is a hydrogen atom, an alkyl group etc., R.sup.51 is an alkyl group or an optionally substituted arylsulfonyl group, R.sup.61 is an alkylamino group or an azido group, or a pharmaceutically acceptable salt thereof.