Answer: There are so many kinds of tulips that it gets confusing. Climate makes a difference too as some will be perennial in one region but not another. Many are truly perennial, and hopefully, these are the kinds you planted.
In general the large-flowered hybrids are less likely to be perennial than the smaller-flowered species or wild types. Some of the best hybrids for naturalizing include the following:
Single early types: 'Keizerkroon', 'Christmas Marvel', and 'Couleur Cardinal';
Triumph types: 'Don Quichotte', 'Golden Melody', 'Kees Nelis', and 'Merry Widow';
Darwin hybrids: all Darwin Hybrids in red, rose, orange, yellow, and two-tone colors.
Fringed tulips: 'Burgundy Lace'
Lily Flowered Tulips: 'Aladdin', 'Maytime', 'Ballade', 'White Triumphator', and 'Red Shine'
Large-flowered but short-statured tulips that naturalize well include:
Kaufmanniana hybrids such as 'Johann Strauss' and 'Stresa'
Fosteriana hybrids such as 'Candela' and 'Red Emperor'
Greigii hybrids such as 'Plaisir' and 'Red Riding Hood'
Small flowered wild or species tulips that naturalize well in cold climates like yours include:
Tulipa bakeri 'Lilac Wonder'
Regarding planting depth, we recommend planting 6 inches deep, or so that 4 inches of soil is above the top of the bulb. Planting deeper, to 8 inches does place the bulbs out of the range of pests such as voles.
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